A hunt after a mare's nest. This chase has two defects: First,
it is very hard to catch the goose; and, secondly, it is of very
little worth when it is caught.
To lead one a wild-goose chase.
beguile one with false hopes, or put one on the pursuit of something
not practicable, or at any rate not worth the chase.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894