Invented by Robert Dicke, the lock-in amplifier is a phase sensitive detector that can extract a signal with a known carrier frequency from an extremely noisy environment. Here we use a single trapped Sr⁺ ion as a quantum lock-in amplifier. We modulate a Zeeman, ground-state, superposition of the ion and are thus able to measure magnetic field fluctuations at the modulation frequency with a, projection noise limited sensitivity bellow 25 pT/√Hz. With a modulation frequency of around one kHz we are thus able to maintain phase coherence up to a time exceeding one second. Using this method we measure the light shift induced by a laser, which is near resonance with a narrow quadruple transition. Light shifts are measured with a, projection-noise limited, sensitivity of 120 mHz.