  We consider a general chaotic inflation model with non-canonical kinetic
term, resulting in attractor solutions for the inflation of quadratic or other
monomial type. In particular, the form of the kinetic term and the potential is
fixed due to the requirement that the inflation model is a quadratic form in
the large field values of the inflaton. We show that a large coupling in the
non-canonical kinetic term allows for the slow-roll inflation with
sub-Planckian field values of the inflaton and the successful predictions of
the quadratic or other monomial type chaotic inflation in light of BICEP2
results are maintained in our model. We find that due to the large rescaling of
the inflaton field in the vacuum, there is no unitarity problem below the
Planck scale.
