Semiconducting half- and, to a lesser extent, full-Heusler compounds are promising thermoelectric materials due to their compelling electronic properties with large power factors. However, intrinsically high thermal conductivity resulting in a limited thermoelectric efficiency has so far impeded their widespread use in practical applications. Here, we report the computational discovery of a class of hitherto unknown stable semiconducting full-Heusler compounds with ten valence electrons ($X_2YZ$, $X$=Ca, Sr, and Ba; $Y$= Au and Hg; $Z$=Sn, Pb, As, Sb, and Bi) through high-throughput $ab-initio$ screening. These new compounds exhibit ultralow lattice thermal conductivity $\kappa_{\text{L}}$ close to the theoretical minimum due to strong anharmonic rattling of the heavy noble metals, while preserving high power factors, thus resulting in excellent phonon-glass electron-crystal materials.