Tony Leung Chiu Wai did not receive an Oscar nomination for portraying Cop 663 in Chungking Express.
Tony Leung the very popular leading man of Hong Kong plays somewhat simple part as the male lead of the second story. Leung plays a beat cop who is somewhat depressed by his recent break up with a flight attendant. He does catch the eye of the new girl at the snack bar named Faye (Faye Wong), who goes on a process to try to cheer him up in a rather odd covert fashion that involves sneaking into the officer's apartment to tidy things up. The majority of Leung's performance is on a fairly steady note of slight depression, this is fitting of the character though and Leung importantly never comes of repetitive despite his character being rather consistent.
Even as a character who is a bit under the weather in terms of his outlook Leung still has an effective charm in the role and he makes the cop quite likable even though he really never seems to be trying to make anyone like him. Leung is enjoyable within the depression of his character. He handles all of his scenes nicely including the ones where he talks to various things around his bathroom as if they were people. He makes the little eccentricity entertaining, and not in anyway over the top as the whole idea sounds. Leung's scenes where he is focused upon are limited though as much of the second story focuses on Faye trying to cheer the cop up.
Leung doesn't have a lot of changes for most of his performance, but this actually is what is best to create the proper dynamic with Faye Wong's peppy performance. They through the differing attitudes creates an effective chemistry that also is believable as well. Most of their scenes together are decidedly not romantic in the traditional fashion, but they all very charming in their own rather peculiar way. Leung is very good in showing how her constant cherry behavior does slowly penetrate the cop's rather thick gloom that keeps him from really enjoying much of anything in his life.
Tony Leung's whole performance in this film does not have many variations, but this actually works best particularly for the last scene of the film. The last scene involves the cop and Faye meeting one more time after some time as passed and she has become a flight attendant and the cop has bought the old snack stand that she use to work out. Leung is very good in this scene as he capitalizes on the rest of his performance by showing the cop finally with a far brighter outlook, and it is a nicely heartfelt scene that gives an appropriately wonderful ending to their story. Leung's work might not be an incredible performance by any means, but like the film itself it is low key but rather endearing.