From Longman Dictionary of Contemporary Englishchance on/upon/across somebody/something phrasal verb formalCHANCE/BY CHANCEto find something or meet someone when you are not expecting to Henry chanced upon some valuable coins in the attic. → chance→ See Verb table
Examples from the Corpus
chance on/upon/across • And the policeman wanted to check his facts before deciding to take a chance on a long shot.• It was well taken, like the rest of his scoring chances on a wet, grey afternoon.• He would just have to take a chance on being interrupted.• Some one will probably take a chance on Bryant anyway, Twardzik said.• He had to take a chance on it.• Cauthen could have a major chance on Spritsail if that horse's poor run at Ascot last week could be ignored.• Five minutes before the break, Jan Molby's pass gave Rob Jones a chance on the edge of the penalty area.• I still had a great chance on the last two holes. 