  Context. Colliding wind binaries are massive systems featuring strong,
interacting stellar winds which may act as particle accelerators. Therefore,
such binaries are good candidates for detection at high energies. However, only
the massive binary Eta Carinae has been firmly associated with a gamma-ray
signal. A second system, gamma^2 Velorum, is positionally coincident with a
gamma-ray source, but unambiguous identification remains lacking. Aims.
Observing orbital modulation of the flux would establish an unambiguous
identification of the binary gamma^2 Velorum as the gamma-ray source detected
by the Fermi Large Area Telescope (Fermi-LAT). Methods. We have used more than
10 years of observations with Fermi-LAT. Events are folded with the orbital
period of the binary to search for variability. Systematic errors that might
arise from the strong emission of the nearby Vela pulsar are studied by
comparing with a more conservative pulse-gated analysis. Results. Hints of
orbital variability are found, indicating maximum flux from the binary during
apastron passage. Conclusions. Our analysis strengthens the possibility that
gamma-rays are produced in gamma^2 Velorum, most likely as a result of particle
acceleration in the wind collision region. The observed orbital variability is
consistent with predictions from recent MHD simulations, but contrasts with the
orbital variability from Eta Carinae, where the peak of the light curve is
found at periastron.
