  We study chaotic dynamics in preheating after inflation in which an inflaton
$\phi$ is coupled to another scalar field $\chi$ through an interaction
$(1/2)g^2\phi^2\chi^2$. We first estimate the size of the quasi-homogeneous
field $\chi$ at the beginning of reheating for large-field inflaton potentials
$V(\phi)=V_0\phi^n$ by evaluating the amplitude of the $\chi$ fluctuations on
scales larger than the Hubble radius at the end of inflation. Parametric
excitations of the field $\chi$ during preheating can give rise to chaos
between two dynamical scalar fields. For the quartic potential ($n=4$,
$V_0=\lambda/4$) chaos actually occurs for $g^2/\lambda <{\cal O}(10)$ in a
linear regime before which the backreaction of created particles becomes
important. This analysis is supported by several different criteria for the
existence of chaos. For the quadratic potential ($n=2$) the signature of chaos
is not found by the time at which the backreaction begins to work, similar to
the case of the quartic potential with $g^2/\lambda \gg 1$.
