  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$_4$.
