The colloquial British-English phrase chance would be a fine thing, and its variants, mean: it would be good if something (stated or implied) were true or likely, but it is not.
This phrase is typically used as a rejoinder, expressing rueful or ironic resignation.
The earliest occurrences of the phrase chance would be a fine thing and variants that I have found are as follows, in chronological order:
1-: From The York Herald (York, Yorkshire, England) of Saturday 20th January 1872:
Police.—At the Borough Police Court, on Wednesday, […] Thomas Watson, beerhouse-keeper, Waterhouse-lane, was charged with keeping open his house for the sale of beer at eleven o’clock on Sunday morning, the 31st December. Mr. Williamson defended. P.C. Bellwood said he visited defendant’s house about eleven o’clock on the morning of the 31st ult., and found two men there, each with a glass of beer. He saw 3d. paid, and called Watson’s attention to it. Watson said he was sorry, and if (witness) would look over it this time, it should not occur again. In cross-examination, the officer said the men were Robert Spanton and Chas. Richardson. He did not meet them in the street and tell them if they went to Watson’s they could get some drink. He saw them both go in. Mr. Williamson then called Robert Spanton who said that Bellwood came to him and Richardson in the street and said, “my lads, you look as though a glass of ale would do you good this morning.” Richardson said that the chance would be a fine thing. Bellwood then told them to go to Watson’s and they would get some. They afterwards went, and Watson gave them a glass of beer each, but no money was paid for it. Sergt. Wake stated that Watson came to him on the morning of the 31st ult. and told him he was sorry that the matter had occurred, and that he would give anything rather than that it should be reported. Mr. Williamson called a man named Jas. Smith, who said that Bellwood had told him to go to Watson’s on the morning in question and he could get some beer. He afterwards heard Bellwood acknowledge that he had sent Spanton and Richardson to Watson’s , and that he would not have reported it but that Sergt. Wake was behind Murgatroyd’s rally. Bellwood denied these statements, and the magistrates fined defendant 20s. and 13s. costs. Mr. Williamson applied for a summons against Bellwood for perjury, which was granted.
2-: From Stray Notes, published in The Preston Chronicle and Lancashire Advertiser (Preston, Lancashire, England) of Saturday 25th September 1880:
“Chance is a fine thing,” and thieves in particular know it. Insane outside pockets make many females conscious of the fact that purses can very easily disappear; and those in charge of Lord Bective’s London residence will, in future, have this as a leading idea—that if they want to preserve the jewellery of the establishment they must see that it is safe. There was recently a great robbery of jewellery at that residence; the thief was captured a few days ago, and he has since confessed that he was tempted to do the job through finding the house “open and totally unprotected.”
3-: From Dyddlyfr Zabulon Dafydd [The Journal of Zabulon Dafydd], published in Yr Herald Cymraeg (Caernarvon, Caernarfonshire, Wales) of Wednesday 6th August 1884—Welsh fel y dywed y Sais means as the English say:
“Chance is a fine thing,” fel y dywed y Sais.
4-: From the transcription of an address that Mr. C. M. Percy, of Wigan, Lancashire, delivered during a meeting of the Leigh Liberal Club—published in The Leigh Chronicle (Leigh, Lancashire, England) of Friday 14th January 1887:
These two parties were working well together, recognising and following harmoniously one leader—Mr. Gladstone 1, the most skilful leader their political life had shown. (Applause.) Then they had the Dissentients, numbering about 75. Some of them were Tories and always had been, and the sooner they followed the example of Mr. Goschen 2—but perhaps they were waiting for similar things, a £5,000 a year—the sooner they followed him the better they would be pleased. (A voice: “Chance is a fine thing.”)
1 William Ewart Gladstone (1809-1898) was a British statesman.
2 George Joachim Goschen (1831-1907) was a British statesman.
5-: From the account of a meeting of the Rural Sanitary Authority, published in The Derbyshire Times (Chesterfield, Derbyshire, England) of Saturday 12th March 1887:
In reply to a member the Clerk said that not more than 30 cwt. could be legally carried on a narrow wheeled cart on the highway. Several members commented on the great injury which was being done to the roads by overloaded carts, and was it decided to make an example of the first offender who could be caught.—Mr. Staley said it was Mr. Wallwin’s extraordinary traffic bill they wanted. (Laughter).—Mr. Wallwin: That is just what we do want.—Mr. Staley: When you are chairman of the County Board we are to have, you will show them.—Mr. Wallwin: Chance is a fine thing. (Laughter).