Precipitation of calcium carbonate in bulk solutions is well known to result in a bell-shaped or bimodal particle size distribution. However, it is unclear how the distribution behaves if precipitation occurs in a small, confined volume. In this Letter, we conduct microfluidic experiments where sodium carbonate and calcium chloride solutions are continuously injected into a microchannel to precipitate calcium carbonate particles. Results show that, regardless of the variations in reagent concentrations, mixing schemes, flow rates, and precipitation time, sizes of precipitated particles in the channel are power law distributed, with an exponent of 1.4. The data are described by an extended Yule process with the introduction of a ripening term. Since the Yule process is a general mechanism for power law generation, the extended Yule process proposed here provides a general model for systems where growth and ripening simultaneously present.