  Shock breakout X-ray emission has been reported for the first time from a
supernova connected with a gamma-ray burst, namely GRB060218/SN2006aj. The
gamma-ray emission and the power-law decaying X-ray afterglow are ascribed to a
highly relativistic jet, while the thermal soft X-rays are thought to be
produced when the radiation-dominated shock breaks from the optically thick
stellar wind. We study the inverse Compton emission of the breakout thermal
soft X-rays scattered by relativistic electrons in the jet forward shock, which
is expected to be at larger radii than the breakout shock. This IC emission
produces sub-GeV to GeV photons, which may be detectable by GLAST. The
detection of such GeV photons simultaneously with the supernova shock breakout
emission would give evidence for the presence of a GRB jet ahead of the shock
while the shock is breaking out. The anisotropic scattering between the X-rays
and relativistic electrons may lead to large angle emission outside of the jet
opening angle. This has implications for the detection of GeV photons from
burstless type Ib/c hypernova shock breakout, which due to its more isotropic
emission might be observed with wide-field X-ray cameras such as LOBSTER.
