We propose a new chemical detection technique in which an analyte's vibrational frequencies are interrogated directly using an array of nanomechanical resonators. This "nanomechanical resonance spectroscopy" (NRS) could permit label-free chemical detection, combining the high sensitivity of nanomechanical approaches with the high selectivity of traditional spectroscopy. A computational proof of principle is presented, demonstrating the central concept: exploiting resonant exchange of vibrational energy for chemical identification. Guidelines for experimental realization of NRS are discussed.