The radical pair reaction underlies the magnetic field sensitivity of chemical reactions and is suggested to play an important role in both chemistry and biology. Current experimental evidence is based on ensemble measurements; however, the ability to probe the radical pair reaction at the single-molecule level would provide valuable information concerning its role in important biological processes. Here, we propose a scheme to detect the charge recombination rate in a radical pair reaction under ambient conditions by using single nitrogen-vacancy center spin in diamond. We demonstrate theoretically that it is possible to detect the effect of the geomagnetic field on the radical pair reaction and propose the present scheme as a possible hybrid model chemical compass.