We report the realization of quantum logic spectroscopy on the 1S0→ 3P0 clock transition of a single 27Al+ ion. This ion is trapped together with a 40Ca+ ion in a linear Paul trap, coupled by Coulomb repulsion, which provides sympathetic Doppler laser cooling and also the means for internal state detection of the clock state of the 27Al+ ion. A repetitive quantum nondemolition measurement is performed to improve the fidelity of state detection. These techniques are applied to obtain clock spectroscopy at approximately 45 Hz. We also perform the preliminary locking on the 1S0 → 3P0 clock transition. Our work is a fundamental step that is necessary toward obtaining an ultra-precision quantum logic clock based on 40Ca+-27Al+ ions.