Nanomechanical oscillators are at the heart of ultrasensitive detectors of force(1), mass(2) and motion(3-7). As these detectors progress to even better sensitivity, they will encounter measurement limits imposed by the laws of quantum mechanics. If the imprecision of a measurement of the displacement of an oscillator(8) is pushed below a scale set by the standard quantum limit, the measurement must perturb the motion of the oscillator by an amount larger than that scale. Here we show a displacement measurement with an imprecision below the standard quantum limit scale. We achieve this imprecision by measuring the motion of a nanomechanical oscillator with a nearly shot-noise limited microwave interferometer(9). As the interferometer is naturally operated at cryogenic temperatures, the thermal motion of the oscillator is minimized, yielding an excellent force detector with a sensitivity of 0.51 aN Hz(-1/2). This measurement is a critical step towards observing quantum behaviour in a mechanical object.