  We consider inflation within the context of what is arguably the simplest
non-metric extension of Einstein gravity. There non-metricity is described by a
single graviscalar field with a non-minimal kinetic coupling to the inflaton
field $\Psi$, parameterized by a single parameter $\gamma$. We discuss the
implications of non-metricity for chaotic inflation and find that it
significantly alters the inflaton dynamics for field values $\Psi \gtrsim
M_P/\gamma$, dramatically changing the qualitative behaviour in this regime.
For potentials with a positive slope non-metricity imposes an upper bound on
the possible number of e-folds. For chaotic inflation with a monomial
potential, the spectral index and the tensor-to-scalar ratio receive small
corrections dependent on the non-metricity parameter. We also argue that
significant post-inflationary non-metricity may be generated.
