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If identical photons meet at a semi-transparent mirror they seem to leave in the same direction, an effect called 'two-photon interference'. It has been known for some time that this effect should occur for photons generated by dissimilar sources with no common history, provided the measurement cannot distinguish between the photons. Here, we report a technique for observing such interference with isolated, unsynchronized sources for which the coherence times differ by several orders of magnitude. In an experiment we cause photons generated by different physical processes, with different photon statistics, to interfere. One of the sources is stimulated emission from a tunable laser, which has Poissonian statistics and a nanoelectronvolt bandwidth. The other is spontaneous emission from a quantum dot in a p-i-n diode with a few-microelectronvolt linewidth. We develop a theory to explain the visibility of interference, which is primarily limited by the timing resolution of our detectors.