The Chase is a 1946 film noir directed by Arthur Ripley and starring Robert Cummings and Peter Lorre.
You can watch The Chase online from Retrovision via Youtube or from the Internet Archive:
The New York Times notes "Peter Lorre is excellent" but says,
it is doubtful whether even the more mature will easily thread through the maze of "The Chase." For this strange and often engrossing melodrama, which came to the Globe on Saturday, besides being almost strangled by its complex plot limps to an irritatingly obvious denouement.