Muon spin relaxation and rotation ($mu$SR) experiments on single crystals of the structurally perfect triangular antiferromagnet YbMgGaO$_4$ indicate the absence of both static long-range magnetic order and spin freezing down to 0.048 K in zero field. Below 0.4 K, the $mu^{+}$ spin relaxation rates, which are proportional to the dynamic correlation function of the Yb$^{3+}$ spins,exhibit temperature-independent plateaus. Same behavior is revealed by temperature-independent local susceptibilities extracted from the Knight shifts of the $mu^{+}$ spin rotation frequencies under a transverse field of 20 Oe. All these $mu$SR results unequivocally support the formation of a gapless U(1) quantum spin liquid ground state in the triangular antiferromagnet YbMgGaO$_4$.
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