Precisely timed detection of single photons plays an important role in the field of quantum information processing and fluorescence sensing. The method of time-correlated single photon counting is therefore constantly evolving and the associated instrumentation is being improved with new ideas and technologies. Simultaneous, time tagged readout of multiple detector channels is invaluable in many applications, spanning from fluorescence lifetime imaging in biology to the measurement of quantum optical correlations in basic research. Here we present a new integrated design, providing up to three independent input channels, a very short dead time, very high throughput, and a timing resolution of 25 ps at reasonable cost and small size. Apart from design features and test results of the instrument, we show an application in quantum optics, namely, the measurement of the photon statistics of a heralded single photon source based on cavity-enhanced spontaneous parametric down-conversion.