The Long Goodbye is Chandler's sixth novel featuring Philip Marlowe, so any of his other works will complement it nicely, particularly with regards to the author's style.
Students may also be interested in reading some of Chandler's screenplay work: Chandler was in high-demand as a screenwriter, and his name is on a number of classic films. It may make for an interesting comparison to see how his writing compares and contrasts between novels and movies.
There is also a film adaptation of The Long Goodbye, which takes the setting into the 1970s. Robert Altman keeps the novel's overarching themes intact, but the stylistic differences between the book and the movie may make for interesting...