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 3 × 10