  We investigate the recently proposed possibility of chaotic inflation with
respect to the imaginary part of the field T in a supersymmetric embedding of
the Starobinsky model. We show that the stage of rapid expansion driven by Im T
in this model ends almost instantly, and the subsequent stages of inflation are
driven by the real part of the field T, as in the standard Starobinsky model.
Thus, the Starobinsky model and its supersymmetric generalizations remain
disfavored by the recent BICEP2 data.
