  Characterization of migration in gravitationally unstable disks is necessary
to understand the fate of protoplanets formed by disk instability. As part of a
larger study, we are using a 3D radiative hydrodynamics code to investigate how
an embedded gas giant planet interacts with a gas disk that undergoes
gravitational instabilities (GIs). This Letter presents results from
simulations with a Jupiter-mass planet placed in orbit at 25 AU within a 0.14
$M_{\odot}$ disk. The disk spans 5 to 40 AU around a 1 $M_{\odot}$ star and is
initially marginally unstable. In one simulation, the planet is inserted prior
to the eruption of GIs; in another, it is inserted only after the disk has
settled into a quasi-steady GI-active state, where heating by GIs roughly
balances radiative cooling. When the planet is present from the beginning, its
own wake stimulates growth of a particular global mode with which it strongly
interacts, and the planet plunges inward six AU in about 10$^3$ years. In both
cases with embedded planets, there are times when the planet's radial motion is
slow and varies in direction. At other times, when the planet appears to be
interacting with strong spiral modes, migration both inward and outward can be
relatively rapid, covering several AUs over hundreds of years. Migration in
both cases appears to stall near the inner Lindblad resonance of a dominant
low-order mode. Planet orbit eccentricities fluctuate rapidly between about
0.02 to 0.1 throughout the GI-active phases of the simulations.
