We have constructed a new type of amplifier whose primary purpose is the readout of superconducting quantum bits. It is based on the transition of an RF-driven Josephson junction between two distinct oscillation states near a dynamical bifurcation point. The main advantages of this new amplifier are speed, high-sensitivity, low back-action, and the absence of on-chip dissipation. Using pulsed microwave techniques, we demonstrate bifurcation amplification in nanofabricated Al junctions and verify that the performance predicted by theory is attained.