  We consider inflation using a class of non-canonical Lagrangians for which
the modification to the kinetic term depends on the field, but not its
derivatives. We generalize the standard Hubble slow roll expansion to the
non-canonical case and derive expressions for observables in terms of the
generalized slow roll parameters. We apply the general results to the
illustrative case of ``Slinky'' inflation, which has a simple, exactly
solvable, non-canonical representation. However, when transformed into a
canonical basis, Slinky inflation consists of a field oscillating on a
multi-valued potential. We calculate the power spectrum of curvature
perturbations for Slinky inflation directly in the non-canonical basis, and
show that the spectrum is approximately a power law on large scales, with a
``blue'' power spectrum. On small scales, the power spectrum exhibits strong
oscillatory behavior. This is an example of a model in which the widely used
solution of Garriga and Mukhanov gives the wrong answer for the power spectrum.
