The colloquial Australian and New-Zealand phrase he (or she, you, etc.) must have killed a Chinaman is used to indicate that a person is suffering from bad luck.

The implication is that this bad luck is punishment for a crime committed by the person.

—Note: This Australian and New-Zealand phrase is unrelated to the U.S. phrase a Chinaman’s chance, which is first recorded in 1893 and denotes a negligible likelihood.

The phrase he (or she, you, etc.) must have killed a Chinaman occurs, for example, in the account of a rugby match between Randwick and Eastern Suburbs, by Phil Wilkins, published in The Sun-Herald (Sydney, New South Wales) of Sunday 24^th August 1997:

As Brial slipped his pass away to flanker Joe Ricciardo and second-rower Tom Bowman speared back into the left corner for the try, Brial fell heavily, probably breaking his wrist.
Brial came off at halftime after his best performance for two months. Later, ruminating on his season’s misfortunes, he said: “I must have killed a Chinaman.”

The earliest occurrences of the phrase he (or she, you, etc.) must have killed a Chinaman that I have found are as follows, in chronological order:

1-: From Kallaàlo. A Sketch in Black for White Men, an unsigned short story published in the Supplement to The Leader: A Weekly Journal of News, Politics, Literature, Science, Agriculture, and Sport (Melbourne, Victoria) of Saturday 31^st October 1885:

Bragan, whose temper did not improve as he lost, cursed his luck from start to finish, urging as a reason the curious non sequitur that “he must have killed a Chinaman.”

2-: From The Daily Telegraph (Launceston, Tasmania) of Saturday 18^th February 1893:

CRICKET.

“St. Ivo” writes with reference to the Geelong v. North Tasmania match:—One of the most interesting and exciting matches ever played on the Cricket Ground was commenced under most inauspicious circumstances on Tuesday morning. Rain, which began to fall about 9 o’clock, continued almost without intermission until mid-day, consequently it was not till after 12 that a start was made. For the seventh time in succession Sidebottom was unfortunate in the spin of the coin, and an impression is now gaining ground amongst Northern cricketers that the genial Tamar skipper must have killed a Chinaman during the winter.

3-: From Association, published in The New Zealand Observer and Free Lance: An Illustrated Journal of Interesting and Amusing Literature (Auckland, New Zealand) of Saturday 21^st July 1894:

Blair played remarkably well, very often passing United’s new back, he ought to have scored, but must have killed a Chinaman.

4-: From the account of a cricket match between England and Australia, published in The Australasian (Melbourne, Victoria) of Saturday 22^nd December 1894:

Lyons was terribly downcast. “I must have killed a Chinaman at some time,” he said in dismay, and if that means ill-luck, one can only wonder what Japanese luck is worth just now.

5-: From Echoes of Sport, by ‘The Vagrant’, published in The Maitland Daily Mercury (Maitland, New South Wales) of Friday 22^nd February 1895:

When some people find things going against them in a manner that is styled “bad luck,” they occasionally emphasize their miserable condition by exclaiming “I must have killed a Chinaman some time or another!” I don’t think Dick Simmons have [sic] ever fallen foul of a follower of Confucius, but if there be any truth in the superstition it looks as if he had.

6-: From the account of five cricket matches that opposed, in Melbourne, “Stoddart’s Eleven, representing England, and a team picked from All Australia”, published in several British newspapers in March 1895—for example in the Evening Telegraph & Star and Sheffield Daily Times (Sheffield, Yorkshire, England) of Friday the 1^st:

Lyons hitherto has done badly against the present team of Englishmen, and this has been attributed partly to a severe attack of influenza which sapped the liveliness of the stalwart hitter, and partly to the fact that he has gone in with an idea that his “luck has been clean out,” as he himself graphically expressed it on the occasion of the first match after Richardson had again and again mowed down his ill-defended wicket. He “must have killed a Chinaman,” a peculiarly cowardly act in his opinion, such as only could merit such a direful retribution.

7-: From the Newcastle Morning Herald and Miners’ Advocate (Newcastle, New South Wales) of Saturday 9^th May 1896:

ATHLETICS.

Ned Pickup, the whilom Newcastle wrestler, must have killed a Chinaman in his time, or else Fate is dead against him. Late papers from Coolgardie show that for the third time he has been disappointed in a match.

8-: From The Border Watch (Mount Gambier, South Australia) of Wednesday 7^th July 1897:

WAS CAIN A CHINAMAN?

Mr. T. C. Daniels, a rhymester, of Wallaroo Mines, thus accounts for the manifold wickedness of the “Heathen Chinee”—“What first set me thinking on this subject was when reading in Genesis iv. 15—‘Therefore whosoever slayeth Cain vengeance shall be taken on him seven-fold.’ Here an old saying occurred to me, ‘He must have killed a Chinaman.’ This is frequently said to or about any person who has been remarkably unfortunate, or the victim of what is commonly called ill-luck. I cannot ascertain where or how the saying originated, but I am inclined to think it was first said shortly after the Lord spake these assuring words to Cain, which to a certain extent guaranteed his safety. And no doubt Cain himself made that part of the Lord’s speech well known, and to this day, although men often kill men, a Chinaman is seldom the victim. They are insulted, beaten, hated, and knocked about, and despised by all, but rarely killed outright. There is something uncanny about killing a Chow that makes even a born murderer to shrink from the job. And the Lord set a mark upon Cain! Now there is no other nation or race of people so easily recognised as Chinamen. The mark must be that strange peculiarity natural to them. . . . But how came the name to be altered from Cain to China? This is an obstacle that has discouraged me for a long time. Now for the way I got over it. . . . The letter A is the key to the riddle. It is first in the alphabet, first in the name of God, Abba; first in Adam; also in Abraham, the first man that God ever blessed with a promise of Christ; the first in Ark; also first in the name of the mount on which the ark rested after the flood, Ararat. The Spirit of God also dwelt in the Ark and Altar was the name given to the place on which sacrifices were offered, and in several other instances of importance too numerous to mention the letter A stands first, and seems to claim a mark of respect. It is to my mind undoubtedly the honoured letter. Now we begin to see through it. The honoured letter was placed second in the name of Cain until after he killed Abel. Now after Cain killed his brother it would seem that the honoured letter, which held second position in his name, was put at the extreme end, and H the first letter of the place of punishment, Hell or Hades, was put where the honoured letter had been, and by this alteration his name was changed from Cain to China!”

9-: From The Colonist (Nelson, New Zealand) of Saturday 13^th November 1897:

WHAT DO THEY SAY?

They say—
[…]
That the weather we’re getting is simply sickening. Someone must have killed a Chinaman. The setting up of a Royal Commission will be the end of it.