There is a growing number of Type IIn supernovae (SNe) which present an outburst prior to their presumably final explosion. These precursors may affect the SN display, and are likely related to poorly charted phenomena in the final stages of stellar evolution. By coadding Palomar Transient Factory (PTF) images taken prior to the explosion, here we present a search for precursors in a sample of 16 Type IIn SNe. We find five SNe IIn that likely have at least one possible precursor event (PTF 10bjb, SN 2010mc, PTF 10weh, SN 2011ht, and PTF 12cxj), three of which are reported here for the first time. For each SN we calculate the control time. We find that precursor events among SNe IIn are common: at the one-sided 99% confidence level, >50% of SNe IIn have at least one pre-explosion outburst that is brighter than 3x10^7^ L_{sun}_ taking place up to 1/3 yr prior to the SN explosion. The average rate of such precursor events during the year prior to the SN explosion is likely >~ 1/yr, and fainter precursors are possibly even more common. Ignoring the two weakest precursors in our sample, the precursors rate we find is still on the order of one per year. We also find possible correlations between the integrated luminosity of the precursor and the SN total radiated energy, peak luminosity, and rise time. These correlations are expected if the precursors are mass-ejection events, and the early-time light curve of these SNe is powered by interaction of the SN shock and ejecta with optically thick circumstellar material.