Magnetic excitations in the quasi-one-dimensional antiferromagnet IPA-CuCl3 are studied by cold neutron inelastic scattering. Strongly dispersive gap excitations are observed. Contrary to previously proposed models, the system is best described as an asymmetric quantum spin ladder. The observed spectrum is interpreted in terms of composite Haldane spin chains. The key difference from actual S=1 chains is a sharp cutoff of the single-magnon spectrum at a certain critical wave vector.