  We present a detailed magnetic study of the triangular antiferromagnet
ErMgGaO$_4$. A point charge calculation under the single ion approximation
reveals a crystal field ground state doublet with a strong Ising-like behavior
of the Er$^{3+}$ moment along the c axis. Magnetic susceptibility and specific
heat measurements indicate no presence of magnetic transitions above 0.5~K and
no evidence of residual entropy as temperature approaching zero. Zero field
(ZF) $\mu$SR measurements shows no sign of static uniform or random field and
longitudinal field (LF) $\mu$SR measurements exhibit persistent spin
fluctuations down to our lowest temperature of 25~mK. Our results provide
evidence of a quantum spin liquid state in the triangular antiferromagnet
ErMgGaO$_4$.
