Optical interferometry is by far the most sensitive displacement measurement technique available, with sensitivities at the 10(-20) m/square root(Hz) level in the large-scale gravitational-wave interferometers currently in operation. Second-generation interferometers will experience a tenfold improvement in sensitivity and be mainly limited by quantum noise, close to the standard quantum limit (SQL), once considered as the ultimate displacement sensitivity achievable by interferometry. In this Letter, we experimentally demonstrate one of the techniques envisioned to go beyond the SQL: amplification of a signal by radiation-pressure backaction in a detuned cavity.