In this inaugural episode of the radio program, Poirot is at his hotel in NY, looking for an apartment. Upon returning to his hotel from the apartment hunting agency,a neighbour requests help opening her door. When Poirot forces it open, he sees the body of a man who's been strangled! It's murder!
By the end of the episode Poirot has his apartment and a new secretary and has solved the case.
Agatha Christie does an intro to the series. It may be worth it for that alone.
I download the episodes through itunes, but they're also available here: