We study the low-energy properties of a Heisenberg spin-1/2 zigzag ladder with different exchange constants on the two chains. Using a nonlinear sigma-model field theory and Abelian bosonization, we find that the excitations are gapless, with a finite spin-wave velocity, if the values of the chain exchanges are small. If the chain exchanges are large, the system is gapped, and the energy spectra of the kink and antikink excitations are different from each other.