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In a two-stage stochastic R&D game, the first mover possesses private information regarding its R&D progress. The rival can only observe its R&D investment, but not the actual R&D position. R&D investment thus carries both investment and signaling effects. Compared with games with complete information, both over and under-investment can occur in equilibrium. We show that private information only matters if the probability of leapfrogging is above a threshold value. Depending on firms' positions, the first mover may engage in signaling by over-investing. The follower therefore may have incentives to under-invest to aviod aggressive responses from the first mover.