My friend Russell reminded me of this film last night. It's charming, and one of the lesser known comedies of both stars. When actress Anna Kalman (Bergman) meets economist Phillip Adams (Grant) it's love at first sight. They begin a whirlwind romance and everything is rosy until an awful truth is revealed - Phillip is a bachelor. In order to protect himself from matrimonially minded females, he has concocted a fictitious wife from whom he is estranged, but cannot be divorced. Anna cannot bear the thought of having been deceived, so she plots her revenge!
Though it's not one of the films that first comes to mind when you think of the two stars, it is still a film that has a place in the public consciousness. It's available on DVD and can be found on YouTube in full, though the uploader has disabled embedding. Click this link to see it: http://youtu.be/fftrNmf21Jo. The clip above features the first meeting of Anna and Phillip and was uploaded by hitchclassic.
Obscurity factor: 4 (known, but not iconic, available on DVD and YouTube)