The results of experimental measurements and theoretical simulations of circular dichroism in the angular distribution (CDAD) of photoemission from atomic core levels of each of the enantiomers of a chiral molecule, alanine, adsorbed on Cu(1 1 0) are presented. Measurements in, and out of, substrate mirror planes allow one to distinguish the CDAD due to the chirality of the sample from that due to a chiral experimental geometry. For these studies of oriented chiral molecules, the CDAD is seen not only in photoemission from the molecular chiral centre, but also from other atoms which have chiral geometries as a result of the adsorption. The magnitude of the CDAD due to the sample chirality differs for different adsorption phases of alanine, and for different emission angles and energies, but is generally small compared with CDAD out of the substrate mirror planes which is largely unrelated to the molecular chirality. While similar measurements of other molecules may reveal larger CDAD due to molecular chirality, the fact that the results for one chiral molecule show weak effects means that such CDAD is unlikely to provide a simple and routine general spectral fingerprint of adsorbed molecular chirality.