  In 2009, Cygnus X-3 (Cyg X-3) became the first microquasar to be detected in
the GeV {\gamma}-ray regime, via the satellites Fermi and AGILE. The addition
of this new band to the observational toolbox holds promise for building a more
detailed understanding of the relativistic jets of this and other systems. We
present a rich dataset of radio, hard and soft X-ray, and {\gamma}-ray
observations of Cyg X-3 made during a flaring episode in 2010 May. We detect a
~3-d softening and recovery of the X-ray emission, followed almost immediately
by a ~1-Jy radio flare at 15 GHz, followed by a 4.3{\sigma} {\gamma}-ray flare
(E > 100 MeV) ~1.5 d later. The radio sampling is sparse, but we use archival
data to argue that it is unlikely the {\gamma}-ray flare was followed by any
significant unobserved radio flares. In this case, the sequencing of the
observed events is difficult to explain in a model in which the {\gamma}-ray
emission is due to inverse Compton scattering of the companion star's radiation
field. Our observations suggest that other mechanisms may also be responsible
for {\gamma}-ray emission from Cyg X-3.
