Gallium-nitride (GaN) is a promising material platform for integrated electro-optic devices due to its wide direct bandgap, pronounced nonlinearities and high optical damage threshold. Low-loss ridge waveguides in GaN layers were recently demonstrated. In this work we provide a first report of four-wave mixing in a GaN waveguide at telecommunication wavelengths, and observe comparatively high nonlinear propagation parameters. The nonlinear coefficient of the waveguide is measured as 1.6 +/- 0.45 [W*m]-1, and the corresponding third-order nonlinear parameter of GaN is estimated as 3.4e-18 +/- 1e-18 [m^2/W]. The results suggest that GaN waveguides could be instrumental in nonlinear-optical signal processing applications.