We report a high-pressure single crystal study of the superconducting ferromagnet UCoGe. Ac-susceptibility and resistivity measurements under pressures up to 2.2 GPa show ferromagnetism is smoothly depressed and vanishes at a critical pressure $p_c = 1.4$ GPa. Near the ferromagnetic critical point superconductivity is enhanced. Upper-critical field measurements under pressure show $B_{c2}(0)$ attains remarkably large values, which provides solid evidence for spin-triplet superconductivity over the whole pressure range. The obtained $p-T$ phase diagram reveals superconductivity is closely connected to a ferromagnetic quantum critical point hidden under the superconducting `dome.
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