  We construct a filtration of chiral Hodge cohomolgy of a K3 surface $X$, such
that its associated graded object is a unitary representation of the N=4 vertex
algebra with central charge $6$ and its subspace of primitive vectors has the
property: its equivariant character for a symplectic automorphism $g$ of $X$
agrees with the McKay-Thompson series for $g$ in Mathieu moonshine.
