Although the unconventional character of the superconductivity in pure and doped UBe 1 3 has been well established, the precise nature of the superconducting order parameter is still unknown. We present muon spin rotation measurements in boron-doped UBe 1 3 showing a paramagnetic frequency shift below the superconducting transition temperature which is nearly independent of applied magnetic field (0.01-0.10 T), unlike a conventional Knight shift. No increase in line width is observed in zero field. These results are compared to observations of the paramagnetic Meissner effect in other superconductors, and are discussed in terms of the possible alignment of spin or orbital moments associated with unconventional superconductivity in this system.