Transition metal oxides of the 4d and 5d block have recently become the targets of materials discovery, largely due to their strong spin-orbit coupling that can generate exotic magnetic and electronic states. Here we report the high pressure synthesis of Lu2Rh2O7, a new cubic pyrochlore oxide based on 4d5 Rh4+ and characterizations via thermodynamic, electrical transport, and muon spin relaxation measurements. Magnetic susceptibility measurements reveal a large temperature-independent Pauli paramagnetic contribution, while heat capacity shows an enhanced Sommerfeld coeﬃcient, γ = 21.8(1) mJ/mol-Rh K2. Muon spin relaxation measurements conﬁrm that Lu2Rh2O7 remains paramagnetic down to 2 K. Taken in combination, these three measurements suggest that Lu2Rh2O7 is a correlated paramagnetic metal with a Wilson ratio of RW = 2.5. However, electric transport measurements present a striking contradiction as the resistivity of Lu2Rh2O7 is observed to monotonically increase with decreasing temperature, indicative of a nonmetallic state. Furthermore, although the magnitude of the resistivity is that of a semiconductor, the temperature dependence does not obey any conventional form. Thus, we propose that Lu2Rh2O7 may belong to the same novel class of non-Fermi liquids as the nonmetallic metal FeCrAs.