We prove a priori estimates for the three-dimensional compressible Euler equations
with moving {\it physical} vacuum boundary, with an equation of state given by $p(\rho) =
C_\gamma \rho^\gamma $ for $\gamma >1$. The vacuum condition necessitates the vanishing
of the pressure, and hence density, on the dynamic boundary, which creates a degenerate and
characteristic hyperbolic {\it free-boundary} system to which standard methods of
symmetrizable hyperbolic equations cannot be applied.