  We introduce Weyl's scale symmetry into the standard model (SM) as a local
symmetry. This necessarily introduces gravitational interactions in addition to
the local scale invariance group \tilde U(1) and the SM groups SU(3) X SU(2) X
U(1). The only other new ingredients are a new scalar field \sigma and the
gauge field for \tilde U(1) we call the Weylon. A noteworthy feature is that
the system admits the St\" uckelberg-type compensator. The \sigma couples to
the scalar curvature as (-\zeta/2) \sigma^2 R, and is in turn related to a St\"
uckelberg-type compensator \varphi by \sigma \equiv M_P e^{-\varphi/M_P} with
the Planck mass M_P. The particular gauge \varphi = 0 in the St\" uckelberg
formalism corresponds to \sigma = M_P, and the Hilbert action is induced
automatically. In this sense, our model presents yet another mechanism for
breaking scale invariance at the classical level. We show that our model
naturally accommodates the chaotic inflation scenario with no extra field.
