We present optical follow-up observations for candidate clusters in the Clusters Hiding in Plain Sight (CHiPS) survey, which is designed to find new galaxy clusters with extreme central galaxies that were misidentified as bright isolated sources in the ROSAT All-Sky Survey catalog. We identify 11 cluster candidates around X-ray, radio, and mid-IR bright sources, including six well-known clusters, two false associations of foreground and background clusters, and three new candidates which are observed further with Chandra. Of the three new candidates, we confirm two newly discovered galaxy clusters: CHIPS1356-3421 and CHIPS1911+4455. Both clusters are luminous enough to be detected in the ROSAT All Sky-Survey data if not because of their bright central cores. CHIPS1911+4455 is similar in many ways to the Phoenix cluster, but with a highly-disturbed X-ray morphology on large scales. We find the occurrence rate for clusters that would appear to be X-ray bright point sources in the ROSAT All-Sky Survey (and any surveys with similar angular resolution) to be 2+/-1%, and the occurrence rate of clusters with runaway cooling in their cores to be <1%, consistent with predictions of Chaotic Cold Accretion. With the number of new groups and clusters predicted to be found with eROSITA, the population of clusters that appear to be point sources (due to a central QSO or a dense cool core) could be around 2000. Finally, this survey demonstrates that the Phoenix cluster is likely the strongest cool core at z<0.7 -- anything more extreme would have been found in this survey.
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