The electromagnetic decays of the ground state baryon multiplets with one heavy quark are calculated using heavy hadron chiral perturbation theory. The M1 and E2 amplitudes for S*-->S gamma, S*-->T gamma and S-->T gamma are separately computed. All M1 transitions are calculated up to O(1/Lambda(chi)(2)). The E2 amplitudes contribute at the same order for S*-->S gamma, while for S*-->T gamma they first appear at O(1/(m(Q)Lambda(chi)(2))) and for S-->T gamma are completely negligible. The renormalization of the chiral loops is discussed and relations among different decay amplitudes are derived. We find that chiral loops involving electromagnetic interactions of the light pseudoscalar mesons provide a sizable enhancement of these decay widths. Furthermore, we obtain an absolute prediction for Gamma(Xi(c)(o)'((*))-->Xi(c)(o)gamma) and Gamma(Xi(b)(-)'((*))-->Xi(b)(-)gamma). Our results are compared to other estimates existing in the literature.