  The notion of chiral symmetry for the conventional Dirac cone is generalized
to include the tilted Dirac cones, where the generalized chiral operator turns
out to be non-hermitian. It is shown that the generalized chiral symmetry
generically protects the zero modes (n=0 Landau level) of the Dirac cone even
when tilted. The present generalized symmetry is equivalent to the condition
that the Dirac Hamiltonian is elliptic as a differential operator, which
provides an explicit relevance to the index theorem.
