The phenomenon of electromagnetically induced quantum coherence is demonstrated between three confined electron subband levels in a quantum well which are almost equally spaced in energy. Applying a strong coupling field, two-photon resonant with the 1-3 intersubband transition, produces a pronounced narrow transparency feature in the 1-2 absorption line. This result can be understood in terms of all three states being simultaneously driven into "phase-locked" quantum coherence by a single coupling field. We describe the effect theoretically with a density matrix method and an adapted linear response theory.