  The interplay between disorder and superconductivity is a subtle and
fascinating phenomenon in quantum many body physics. The conventional
superconductors are insensitive to dilute nonmagnetic impurities, known as the
Anderson's theorem. Destruction of superconductivity and even
superconductor-insulator transitions occur in the regime of strong disorder.
Hence disorder-enhanced superconductivity is rare and has only been observed in
some alloys or granular states. Because of the entanglement of various effects,
the mechanism of enhancement is still under debate. Here we report
well-controlled disorder effect in the recently discovered monolayer NbSe$_2$
superconductor. The superconducting transition temperatures of NbSe$_2$
monolayers are substantially increased by disorder. Realistic theoretical
modeling shows that the unusual enhancement possibly arises from the
multifractality of electron wave functions. This work provides the first
experimental evidence of the multifractal superconducting state.
