We report evidence for unconventional superconductivity in CeIn3 at a pressure P=2.65 GPa above the critical pressure (P(c)similar to2.5 GPa) revealed by measurements of the nuclear-spin-lattice-relaxation time (T-1) and ac susceptibility (ac-chi). Both measurements of T-1 and ac-chi have pointed to a superconducting transition at T-c=95 mK, which is much lower than the onset temperature T-onset=0.15 K at zero resistance. The temperature dependence of 1/T-1 shows no coherence peak just below T-c, indicative of an unconventional nature for the superconductivity induced in CeIn3.