We report the operation and characterization of an upconversion random laser emitting at 560 nm, when directly pumped by three photon excitation at the near IR wavelength of 1350 nm in a colloidal dye solution in the weakly scattering regime. Using a special dye with a high three-photon cross-section and TiO(2) nanoparticles (250 nm diameter), optimized upconverted emission was obtained for particle densities of ~2 x 10(9)/cm3. A strong dependence on the nanoparticle concentration and the pumping area was verified. The presence of spikes with linewidths ~0.4 nm in the emitted spectrum is the signature of coherent emission from this three-photon pumped random laser.