We study the X-ray magnetic circular dichroism (XMCD) spectra at the U M 4,5 and N 4,5 edges of uranium monochalcogenides, UX where X=S, Se, and Te, examining the applicability of the XMCD sum rules to UX by the fully relativistic full-potential linearcombination-of-atomic-orbitals method based on the density functional theory. To extract the transitions relevant to the sum-rule analysis, we employ the Mulliken population analysis (MPA). Using the MPA, the orbital sum rule is found to be valid to 10-20 % for the M 4,5 edges and valid to 5-15 % for the N 4,5 edges. On the other hand, the spin sum rule is found to be valid to 10-20 % for the M 4,5 edges whereas valid to 30-35 % for the N 4,5 edges. Furthermore, it is found that the calculated XMCD spectra are consistent with a recent experimental observation that the intensity of the N 4,5 XMCD signal is comparable to that of the M 4,5 XMCD signal although contradicting a previous theoretical prediction that the XMCD intensity at the N 4,5 edges is one order of magnitude smaller than that at the M 4,5 edges.