A highly anisotropic superconducting gap is found in single crystals of FeSe by studying the London penetration depth Δλ measured down to 50 mK in samples before and after 2.5 MeV electron irradiation. The gap minimum increases with introduced pointlike disorder, indicating the absence of symmetry-imposed nodes. Surprisingly, the superconducting transition temperature Tc increases by 0.4 K from Tc0≈8.8 K while the structural transition temperature Ts decreases by 0.9 K from Ts0≈91.2 K after electron irradiation. We discuss several explanations for the Tc enhancement and propose that local strengthening of the pair interaction by irradiation-induced Frenkel defects most likely explains the phenomenon.