The American-English phrase a chicken in every pot (and a car in every garage), and its variants, mean enough food, wealth, etc., for the whole population to share or participate in the benefits; prosperity for everyone.

The phrase a chicken in every pot originated in a declaration famously attributed to Henri de Bourbon (1553-1610), King of Navarre as Henri III (1572-1610), and King of France as Henri IV (1589-1610).

The earliest occurrence that I have found of this purported declaration is from Histoire du roy Henry le Grand (Paris: Edme Martin, 1662), by the French cleric Hardouin de Péréfixe de Beaumont (1606-1671):

Si Dieu me donne encore de la vie je feray qu’il n’y aura point de laboureur en mon Royaume, qui n’ait moyen d’auoir vne poule dans son pot.
     translation:
If God gives me more life I will make sure that no peasant in my realm will lack the means to have a chicken in his pot.

Among the many mentions of the declaration attributed to Henri IV, the following is from The Influence of Free Trade upon the Condition of the Labouring Classes, an unsigned article published in Blackwood’s Edinburgh Magazine (Edinburgh: William Blackwood; London: Thomas Cadell) of April 1830:

If he [= “the real friend of the industrious poor”] cannot absolutely realise the benevolent and amiable wish of Henry IV., that every peasant may have his chicken in his pot on Sunday, he will at least endeavour to render him independent of the charity of others, and relieve him from absolute want.

The extended phrase a chicken in every pot and a car in every garage appeared in 1928 in the context of the U.S. presidential campaign. The Republican nominee, Herbert Clark Hoover (1874-1964), who was to become the 31^st President of the USA (1929-33), centred his campaign on the achievements of the Republican statesman John Calvin Coolidge (1872-1933), 30^th President of the USA (1923-29).

In October 1928, the Republican Party took out full-page advertisements in newspapers—for example in the Pittsburgh Sun-Telegraph (Pittsburgh, Pennsylvania) of Saturday 20^th—advertisements titled A Chicken for Every Pot, and declaring:

Republican prosperity has reduced hours and increased earning capacity, silenced discontent, put the proverbial “chicken in every pot.” And a car in every backyard, to boot.

Hoover used a similar metaphor in a speech that he delivered on Monday 22^nd October 1928, at Madison Square Garden, New York City—as transcribed in The Sun (Baltimore, Maryland) of Tuesday 23^rd October 1928:

Our people are steadily increasing their spending for higher standards of living. Today there are almost nine automobiles for each ten families where seven and a half years ago only enough were running to average less than four automobiles for each ten families. The slogan of progress is changing from the full dinner pail [cf. footnote] to the full garage.

The following passage from an article about the necessity for a Federal system of old-age pensions, published in The Sun (Baltimore, Maryland) of Saturday 22^nd December 1928, shows how a chicken in every pot and a car in every garage came to be used as a phrase—the reference to its origin being here implicit:

It is a subject which must appeal deeply to every person who takes any thought for the future, and it requires serious study. “A chicken in every pot and a car in every garage” has a distinctly hollow sound while such human problems as this remain.

 

Note: The Republican statesman William McKinley (1843-1901), 25^th President of the USA (1897-1901), used the slogan a full dinner pail to promote his promise of prosperity for all during the 1896 presidential campaign. The slogan was used again by Republican candidates during the 1900, 1904 and 1908 presidential campaigns. During the 1912 campaign, the Democrats contrasted the full dinner pail with the housewife’s empty market basket, caused by Republican tariffs on many necessities.
—Illustration: In the following cartoon, titled The Campaign Issue, published in Puck (New York: Keppler & Schwarzmann) of Wednesday 1^st May 1912, the U.S. cartoonist Udo J. Keppler (1872-1956) depicted the Republican elephant G.O.P. holding an empty bucket labelled The Dinner Pail and Mrs Consumer holding an empty basket labelled Tariff Tax on the Necessities of Life—the caption is:

The Republican Elephant.—Well, the campaign is on. Fill the Dinner-Pail for me.
The Woman in the Case.—You great big Gop! How can I give you a Full Dinner-Pail from an Empty Market-Basket?