  In this paper we continue our study of the tree level MHV graviton scattering
amplitudes from the point of view of celestial holography. In arXiv:2008.04330
we showed that the celestial OPE of two gravitons in the MHV sector can be
written as a linear combination of $\overline{SL(2,\mathbb C)}$ current algebra
and supertranslation descendants. In this note we show that the OPE is in fact
manifestly invariant under the infinite dimensional Virasoro algebra as is
expected for a $2$-D CFT. This is consistent with the conjecture that the
holographic dual in $4$-D asymptotically flat space time is a $2$-D CFT. Since
we get only one copy of the Virasoro algebra we can conclude that the
holographic dual theory which computes the MHV amplitudes is a chiral CFT with
a host of other infinite dimensional global symmetries including
$\overline{SL(2,\mathbb C)}$ current algebra, supertranslations and
subsubleading soft graviton symmetry. We also discuss some puzzles related to
the appearance of the Virasoro symmetry.
