  We calculate analytically and numerically the production of superheavy dark
matter (X) when it is coupled to the inflaton field \phi within the context of
a slow-roll m_\phi^2 \phi^2/2 inflationary model with coupling g^2 X^2
\phi^2/2. We find that X particles with a mass as large as 1000 H_i, where H_i
is the value of the Hubble expansion rate at the end of inflation, can be
produced in sufficient abundance to be cosmologically significant today. This
means that superheavy dark matter may have a mass of up to 10^{-3} Planck mass.
We also derive a simple formula that can be used to estimate particle
production as a result of a quantum field's interaction with a general class of
homogeneous classical fields. Finally, we note that the combined effect of the
inflaton field and the gravitational field on the X field causes the production
to be a nonmonotonic function of g^2.
