  The rapidly improving precision of measurements of gravitational lensing of
the Cosmic Microwave Background (CMB) also requires a corresponding increase in
the precision of theoretical modeling. A commonly made approximation is to
model the CMB deflection angle or lensing potential as a Gaussian random field.
In this paper, however, we analytically quantify the influence of the
non-Gaussianity of large-scale structure lenses, arising from nonlinear
structure formation, on CMB lensing measurements. In particular, evaluating the
impact of the non-zero bispectrum of large-scale structure on the relevant CMB
four-point correlation functions, we find that there is a bias to estimates of
the CMB lensing power spectrum. For temperature-based lensing reconstruction
with CMB Stage-III and Stage-IV experiments, we find that this lensing power
spectrum bias is negative and is of order one percent of the signal. This
corresponds to a shift of multiple standard deviations for these upcoming
experiments. We caution, however, that our numerical calculation only evaluates
two of the largest bias terms and thus only provides an approximate estimate of
the full bias. We conclude that further investigation into lensing biases from
nonlinear structure formation is required and that these biases should be
accounted for in future lensing analyses.
