  We report the Fermi Large Area Telescope discovery of gamma-ray pulsations
from the 22.7 ms pulsar A in the double pulsar system J0737-3039A/B. This is
the first mildly recycled millisecond pulsar (MSP) detected in the GeV domain.
The 2.7 s companion object PSR J0737-3039B is not detected in gamma rays. PSR
J0737-3039A is a faint gamma-ray emitter, so that its spectral properties are
only weakly constrained; however, its measured efficiency is typical of other
MSPs. The two peaks of the gamma-ray light curve are separated by roughly half
a rotation and are well offset from the radio and X-ray emission, suggesting
that the GeV radiation originates in a distinct part of the magnetosphere from
the other types of emission. From the modeling of the radio and the gamma-ray
emission profiles and the analysis of radio polarization data, we constrain the
magnetic inclination $\alpha$ and the viewing angle $\zeta$ to be close to
90$^\circ$, which is consistent with independent studies of the radio emission
from PSR J0737-3039A. A small misalignment angle between the pulsar's spin axis
and the system's orbital axis is therefore favored, supporting the hypothesis
that pulsar B was formed in a nearly symmetric supernova explosion as has been
discussed in the literature already.
