The E-2 --> (4)A(2) emission of Cr3+ in crystals and glasses is of great importance in science and technology. We report a new excitation mode for this emission in Y3Ga5O12 (YGG) codoped with Cr3+ and Yb3+. It is based on an upconversion mechanism using F-2(5/2) Of Yb3+ as an intermediate state. Excitation in the near-IR at 969.6 nm leads to visible luminescence around 700 nm at low temperature. In YGG:2%Cr3+,1%Yb3+ at 15 K and for a laser power of 150 mW the efficiency of the process is 5.5%. From its time dependence the upconversion mechanism is found to be dominated by an energy transfer step: Two excited Yb3+ ions simultaneously transfer their F-2(5/2) excitation to Cr3+.