We report the properties of two new isostructural compounds, U3Bi4Ni3 and U3Bi4Rh3. The first of these compounds is non-metallic, and the second is a nearly ferromagnetic metal, both as anticipated from their electron count relative to other U-based members of the larger 3-4-3 family. For U3Bi4Rh3, a logarithmic increase of C/T below 3 K, a resistivity proportional to T^4/3, and the recovery of Fermi-liquid behavior in both properties with applied fields greater than 3T, suggest that U3Bi4Rh3 may be a new example of a material displaying ferromagnetic quantum criticality.