  The Busemann-Petty problem asks whether origin-symmetric convex bodies in
real Euclidean n-space with smaller central hyperplane sections necessarily
have smaller volume. The answer is affirmative for n less or equal to 4 and
negative if n greater or equal to 5. We study this problem in the complex
hyperbolic n-space and prove that the answer is affirmative for n less or equal
to 2 and negative for n greater or equal to 3.
