  We study the polymer quantization of a homogeneous massive scalar field in
the early universe using a prescription inequivalent to those previously
appearing in the literature. Specifically, we assume a Hilbert space for which
the scalar field momentum is well defined but its amplitude is not. This is
closer in spirit to the quantization scheme of loop quantum gravity, in which
no unique configuration operator exists. We show that in the semi-classical
approximation, the main effect of this polymer quantization scheme is to
compactify the phase space of chaotic inflation in the field amplitude
direction. This gives rise to an effective scalar potential closely resembling
that of hybrid natural inflation. Unlike polymer schemes in which the scalar
field amplitude is well-defined, the semi-classical dynamics involves a past
cosmological singularity; i.e., this approach does not mitigate the big bang.
