  We present the first lattice calculation of the valence-quark generalized
parton distribution (GPD) of the pion using the large-momentum effective theory
(LaMET) approach. We focus on the zero-skewness limit, where the GPD has a
probability-density interpretation in the longitudinal Bjorken $x$ and the
transverse impact-parameter distributions. Our calculation is done using clover
valence fermions on an ensemble of gauge configurations with $2+1+1$ flavors
(degenerate up/down, strange and charm) of highly improved staggered quarks
(HISQ) with lattice spacing $a \approx 0.12$ fm, box size $L \approx 3$ fm and
pion mass $m_\pi \approx 310$ MeV. The parton distribution function and the
form factor are reproduced as special limits of the GPD as expected. Due to the
large errors, this exploratory study does not show a clear preference among
different model assumptions about the kinematic dependence of the GPD. To
discriminate between these assumptions, future studies using higher-statistics
data will be crucial.
