1
general::
A futile search or pursuit, as in I think she sent us on a wild goose chase looking for their beach house. This idiom originally referred to a form of 16th-century horseracing requiring riders to follow a leader in a particular formation (presumably resembling a flock of geese in flight). Its figurative use dates from about 1600.
American Heritage Idioms
2
general::
Phrase(s): a wild-goose chase
a worthless hunt or chase; a futile pursuit. • I wasted all afternoon on a wild-goose chase. • John was angry because he was sent out on a wild-goose chase.
McGrawhill's American Idioms And Phrasal Verbs