When measuring the position of a mechanical oscillator, quantum mechanics imposes a strict limit on the attainable precision: Any reduction of imprecision leads to increased quantum backaction of the measuring probe on the oscillator. This quantum limit can be circumvented, in principle allowing to indefinitely reduce imprecision, by monitoring only a single quadrature of the oscillator. Such backaction-evading measurement has been recently demonstrated in electromechanical oscillators coupled to microwave resonant circuits. Here we demonstrate this technique in a photonic crystal nanomechanical oscillator, cryogenically and optomechanically cooled to a few quanta.