The obsolete British-English phrase choke, chicken: more are hatching, and its variants, were said to console a child choking over his or her food—as explained in Folk-Phrases, published in The Globe and Traveller (London, England) of Friday 21st February 1890:
A peculiar phrase is addressed to choking children. “Choke up chicken, more a hatching”—the meaning of the latter part of the sentence is scarcely clear to-day.
The earliest occurrence of the phrase that I have found is from A Complete Collection of Genteel and Ingenious Conversation, according to the Most Polite Mode and Method now used at Court, and in the Best Companies of England, by the Irish satirist, poet and Anglican cleric Jonathan Swift (1667-1745). Published in London in 1738 but composed in the first decade of the 18th century, this book is a satire on the use of clichés; its purported author, Simon Wagstaff, assures “the Reader, that there is not one single witty Phrase in this whole Collection, which hath not received the Stamp and Approbation of at least one hundred Years” (cf. in this regard the authentic origin of ‘to rain cats and dogs’):
[—Colonel coughing.—
Col. I have got a sad Cold.
[…]
Miss. [to Col.] Choak, Chicken; there’s more a hatching.
In A Classical Dictionary of the Vulgar Tongue (London: Printed for S. Hooper, 1788), the English antiquary and lexicographer Francis Grose (1731-1791) recorded two different phrases under choak:
Choak. Choak away, the church yard’s near; a jocular saying to a person taken with a violent fit of coughing, or who has swallowed any thing, as it is called, the wrong way. Choak, chicken, more are hatching; a like consolation.
The former phrase had already appeared in “Proverbs communicated by Mʳ Andrew Paschall of Chedsey in Somersetshire”, published by the English naturalist and theologian John Ray (1627-1705) in A Collection of English Proverbs Digested into a convenient Method for the speedy finding any one upon occasion; with Short Annotations. Whereunto are added Local Proverbs with their Explications, Old Proverbial Rhythmes, Less known or Exotick Proverbial Sentences, and Scottish Proverbs (Cambridge: Printed by John Hayes, Printer to the University, for W. Morden, 1678):
Choak up, the Church-yard’s nigh.
The phrase then occurs as choak, chicken: there are more hatching in Letter I. To Lord Viscount Folkestone. On the Proceedings in Parliament, during the Session of 1819, relative to the Paper Money, dated “North Hampstead, Long Island, 11 July 1819”, by William Cobbett 1, published in Cobbett’s Weekly Political Register (London, England) of Saturday 18th September 1819:
“Choak, chicken: there are more hatching:” say the women to the sulky babies, when they are heaving out tears and sighs.
1 William Cobbett (1763-1835) was an English author and political reformer; he founded the periodical Cobbett’s Political Register in 1802.
The following is from an article about the British Conservative politician George Smythe (1818-1857), published in The Globe and Traveller (London, England) of Tuesday 13th July 1847:
Mr. Smythe […] is more afraid of being “choked with the chickweed of the status quo, than of being overwhelmed with a torrent of revolutionary reform.” Perhaps it is a natural apprehension—that of being “choked with chickweed.” Malice might retort “Choke chicken—there’s more a hatching.”
The phrase occurs in the following from Notes and Queries: A Medium of Intercommunication for Literary Men, General Readers, etc. (London: Published at the Office, 43 Wellington Street, Strand, W.C.) of Saturday 7th January 1871:
Shropshire Sayings.—An old lady, who was the daughter of a Salopian farmer, and who died not long since at the age of seventy-eight, was accustomed to make use of the following sayings, which had been current in her early days in her native county. Some of them are curious, and may be found interesting:—
“Choke chicken, more hatching.” A variation of the proverb, that “As good fish remain in the sea as ever came out of it.”
“Noble as the race of Shenkin 2 and line of Harry Tudor.”
“He smiles like a basket of chips”; i.e. of habit and unconsciously.
“Useful as a shin of beef, which has a big bone for the big dog, a little bone for the little dog, and a sinew for the cat.”
“It’s all on one side like Bridgnorth election.” 3
“Ahem! as Dick Smith said when he swallowed the dishclout,” signifying that troubles should be borne with fortitude.
“All friends round the wrekin.” 4
Wm. Underhill.
2 There is an old Welsh song titled Of Noble Race was Shenkin.
3 The phrase it’s all on one side like Bridgnorth election was explained in The Staffordshire Advertiser (Stafford, Staffordshire, England) of Saturday 2nd May 1818:
The borough of Bridgnorth, in Shropshire, […] from its uniformly quiet and undisputed Parliamentary Elections, has given rise to a well-known provincial adage, (like a Bridgnorth Election, all on one side).
4 The phrase (all) round the Wrekin, or wrekin, means by a circuitous route, hence also, figuratively, in a lengthy, rambling or roundabout manner (Wrekin is the name of a prominent hill in the east of Shropshire, a county of England, situated on the border with Wales).
—Cf. to go (all) round the houses and to go round Robin Hood’s barn.
word histories 
My sister and I grew up hearing, “Choke-up, Chicken” whenever we coughed. It became so ingrained in our family that neither of my parents could recall where it came from. Since my Father’s parents were both born in London, England in 1886, this explains a lot. Now I can offer an explanation when people look at me funny after I’ve said it automatically when I hear someone coughing.
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