We propose a new model for the initiation of a solar coronal mass ejection (CME). The model agrees with two properties of CMEs and eruptive flares that have proved to be very difficult to explain with previous models: (1) very low-lying magnetic field lines, down to the photospheric neutral line, can open toward infinity during an eruption; and (2) the eruption is driven solely by magnetic free energy stored in a closed, sheared arcade. Consequently, the magnetic energy of the closed state is well above that of the posteruption open state. The key new feature of our model is that CMEs occur in multipolar topologies in which reconnection between a sheared arcade and neighboring flux systems triggers the eruption. In this "magnetic breakout" model, reconnection removes the unsheared field above the low-lying, sheared core flux near the neutral line, thereby allowing this core flux to burst open. We present numerical simulations that demonstrate our model can account for the energy requirements for CMEs. We discuss the implication of the model for CME/flare prediction.