The phrase wild-goose chase denotes an absurd or hopeless pursuit.

But its original sense was entirely different; it was defined as follows in The Century Dictionary (New York, 1904):

a kind of horse-race, in which two horses were started together, the rider who gained the lead forcing the other to follow him wherever he chose to go.

In The Hunter. A Discourse of Horsemanship: Directing the right way to breed, keep, and train a Horse, for ordinary Hunting and Plates (Oxford, 1685), Nicholas Cox (floruit 1673-1731) explained why that kind of horse race was named wild-goose chase and what it consisted in:

The Wildgoose Chase received its Name from the manner of the flight which is made by Wildgeese, which is generally one after another: so the two Horses after the running of Twelvescore Yards, had liberty, which Horse soever could get the leading, to ride what ground he pleas’d; the hindmost Horse being bound to follow him, within a certain distance agreed on by Articles, or else to be whipt up by the Triers or Judges which rode by, and which ever Horse could distance the other won the Match.

The phrase wild-goose chase is first recorded in its original sense, but as part of an extended horse-racing metaphor, in An excellent conceited Tragedie of Romeo and Iuliet (London, 1597), by the English poet and playwright William Shakespeare (1564-1616); in Act 2, scene 4, Mercutio, who is losing a duel of wits with Romeo, asks Benvolio to intervene; but Romeo says that he will declare himself the winner if Mercutio gives up; in response to Romeo’s use of the horse-riding phrase switch and spurs, meaning at full speed (switch designates a slender tapering riding whip), Mercutio uses the image of a wild-goose chase:

– Mercutio: Come between vs good Benuolio, for my wits faile.
– Romeo: Swits and spurres, swits & spurres, or Ile cry a match.
– Mercutio: Nay if thy wits runne the wildgoose chase, I haue
done: for I am sure thou hast more of the goose in one of
thy wits, than I haue in al my fiue: Was I with you there for
the goose?
– Romeo: Thou wert neuer with me for any thing, when
thou wert not with me for the goose.
– Mercutio: Ile bite thee by the eare for that iest.
– Romeo: Nay good goose bite not.
– Mercutio: Why thy wit is a bitter sweeting, a most sharp sauce
– Romeo: And was it not well seru’d in to a sweet goose?
– Mercutio: Oh heere is a witte of Cheuerell that stretcheth
from an ynch narrow to an ell broad.
– Romeo: I stretcht it out for the word broad, which added to
the goose, proues thee faire and wide a broad goose.

The phrase came to be used figuratively in the sense of an erratic course taken by a person, especially in following their own impulses, as in this passage from The Spanish Gipsie (London, 1653), a tragicomedy first performed in 1623 and attributed to the English playwrights Thomas Middleton (1580-1627) and William Rowley (circa 1585-1626)—fegary is an alteration of vagary:

Enter Diego.
– Diego: Ha, ha, ha! some one
That hath slept well to night, should a but see mee
Thus merry by my selfe, might justly think
I were not well in my wits.
– Lewys: Diego!
– Diego: Yes ’tis I, and I have had a fine fegary,
The rarest, Wild-goose chase.

The current sense of wild-goose chase arose both from this figurative usage and from the fact that, when the origin of the phrase was forgotten, it was reinterpreted as referring to the chasing of a wild goose; this is clear from the definition of wild-goose chase in A Dictionary of the English Language (London, 1755), by the English lexicographer Samuel Johnson (1709-84):

a pursuit of something as unlikely to be caught as the wildgoose.

This reinterpretation has continued up to the present day, as shown by the definition of wild-goose chase in Webster’s New World College Dictionary (4^th edition – © 2010 by Houghton Mifflin Harcourt):

any search, pursuit, or endeavor regarded as being as futile as trying to catch a wild goose by chasing it.

The following also shows how the origin of the phrase came to be reinterpreted; in The Sporting Dictionary, and Rural Repository of General Information upon every Subject appertaining to the Sports of the Field (London, 1803), the veterinary surgeon and author William Taplin (died 1807) correctly defined wild-goose chase as a horse-racing phrase but, not knowing that it originally referred to the flight of wild geese, wrote that it is a metaphor for something unlikely to be attained:

Wild-goose chase,—is neither more or less than a metaphorical allusion to the uncertainty of its termination. This originated in a kind of chase (more properly match) formerly decided in the following way. Two horses having started at the place appointed, continued to rate by the side of each other, till one having obtained the lead, was entitled to proceed in whatever direction the rider pleased, (either by shortening or prolonging the distance to the winning spot previously agreed on,) according to the qualifications of his horse.