  We report on first observation of spin noise in a strongly birefringent
semiconductor -- halide perovskite single crystal MAPbI$_3$. The observed spin
noise resonance is ascribed to free holes with a record spin dephasing time of
4 ns. The spin dynamics is found to be affected by the residual light
absorption of the crystal providing renormalization of the Larmor frequency.
Extended spin noise spectroscopy with rotating magnetic field allowed us not
only to evaluate the $g$-factor anisotropy, but also to distinguish two
different spin subsystems tentatively associated to twinning of the crystal.
