A source of triggered entangled photon pairs is a key component in quantum information science; it is needed to implement functions such as linear quantum computation, entanglement swapping and quantum teleportation. Generation of polarization entangled photon pairs can be obtained through parametric conversion in nonlinear optical media or by making use of the radiative decay of two electron-hole pairs trapped in a semiconductor quantum dot. Today, these sources operate at a very low rate, below 0.01 photon pairs per excitation pulse, which strongly limits their applications. For systems based on parametric conversion, this low rate is intrinsically due to the Poissonian statistics of the source. Conversely, a quantum dot can emit a single pair of entangled photons with a probability near unity but suffers from a naturally very low extraction efficiency. Here we show that this drawback can be overcome by coupling an optical cavity in the form of a 'photonic molecule' to a single quantum dot. Two coupled identical pillars-the photonic molecule-were etched in a semiconductor planar microcavity, using an optical lithography method that ensures a deterministic coupling to the biexciton and exciton energy states of a pre-selected quantum dot. The Purcell effect ensures that most entangled photon pairs are emitted into two cavity modes, while improving the indistinguishability of the two optical recombination paths. A polarization entangled photon pair rate of 0.12 per excitation pulse (with a concurrence of 0.34) is collected in the first lens. Our results open the way towards the fabrication of solid state triggered sources of entangled photon pairs, with an overall (creation and collection) efficiency of 80%.