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Abstract 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 SL 2 ℂ ¯ $$ \overline{\mathrm{SL}\left(2,\mathbb{C}\right)} $$ 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 SL 2 ℂ ¯ $$ \overline{\mathrm{SL}\left(2,\mathbb{C}\right)} $$ current algebra, supertranslations and subsubleading soft graviton symmetry. We also discuss some puzzles related to the appearance of the Virasoro symmetry.