  The formula for the Hirzebruch $\chi_y$-genus of complex manifolds is a
consequence of the Hirzebruch-Riemann-Roch formula. The classical index
formulae for Todd genus, Euler number, and Signature correspond to the case
when the complex variable $y=$ 0, -1, and 1 respectively. Here we give a {\it
direct} derivation of this nice formula based on supersymmetric quantum
mechanics.
