Black prisms of UFeS(3) and UFeSe(3) have been synthesized by solid-state reactions of U, Fe, and S or Se with CsCl as a flux at 1173 K. The structure of these isostructural compounds consists of layers of edge- and corner-sharing FeS(6) or FeSe(6) octahedra that are separated by layers of face- and edge-sharing US(8) or USe(8) bicapped trigonal prisms. The isomer shifts in the iron-57 Mössbauer spectra of both UFeS(3) and UFeSe(3) are consistent with the presence of high-spin iron(II) ions octahedrally coordinated to S or Se. The XANES spectra of UFeS(3) and UFeSe(3) are consistent with uranium(IV). Single-crystal magnetic susceptibility measurements along the three crystallographic axes of UFeSe(3) reveal a substantial magnetic anisotropy with a change of easy axis from the a-axis above 40 K to the b-axis below 40 K, a change that results from competition between the iron(II) and uranium(IV) anisotropies. The temperature dependence of the magnetic susceptibility along the three axes is characteristic of two-dimensional magnetism. A small shoulder-like anomaly is observed in the magnetic susceptibilities along the a- and b-axes at 96 and 107 K, respectively. Below 107 K, the iron-57 Mössbauer spectra of UFeS(3) and UFeSe(3) show that the iron nuclei experience a magnetic hyperfine field that results from long-range magnetic ordering of at least the iron(II) magnetic moments because the field exhibits Brillouin-like behavior. Below 40 K there is no significant change in the Mössbauer spectra as a result of change in magnetic anisotropy. The complexity of the iron-57 Mössbauer spectra and the temperature and field dependencies of the magnetic properties point toward a complex long-range magnetic structure of two independent iron(II) and uranium(IV) two-dimensional sublattices. The temperature dependence of the single-crystal resistivity of UFeSe(3) measured along the a-axis reveals semiconducting behavior between 30 and 300 K with an energy gap of about 0.03 eV below the 53 K maximum in susceptibility, of about 0.05 eV between 50 and 107 K, and of 0.03 eV above 107 K; a negative magnetoresistance was observed below 60 K.