outside chance

plural outside chances

1. idiomaticA small likelihood; a remote possibility.

   Then, perhaps, there may be a chance of detecting him; but it's an outside chance.

   1886, Andrew Lang, chapter 7, in The Mark Of Cain

   2 more examples

   Harry Truman might get a good share of the popular vote, but few people, outside of Harry Truman, gave him even an outside chance of getting the electoral votes necessary for election.

   1948 October 25, "The Nation: The Real Fight," Time (retrieved 29 Jan 2019)

   Given talent and the right connections, opera composers have at least an outside chance of a premiere performance by a reputable opera company.

   2008 February 23, Bernard Holland, "Music Review: A Visit That Crosses Two Centuries and an Ocean," New York Times (retrieved 29 Jan 2019)