The BPS spectrum of string theory on AdS(3) x S-3 x S-3 x S-1 is determined using a world -sheet description in terms of WZW models. It is found that the theory only has BPS states with j(+) = j(-) where j(+) refer to the spins of the zu(2) algebras of the large N = 4 superconformal algebra. We then re-examine the BPS spectrum of the corresponding supergravity and find that, contrary to previous claims in the literature, also in supergravity only the states with j(+) = j(-) are BPS. This resolves a number of long-standing puzzles regarding the BPS spectrum of string theory and supergravity in this background.
