CFPB Data Collection Security Act - Amends the Consumer Financial Protection Act of 2010 to direct the Consumer Financial Protection Bureau (CFPB) to: (1) establish an opt-out list of consumers who have notified the CFPB that they do not wish to allow it to collect personally identifiable information about them, and (2) give consumers a method of adding and removing their names from the opt-out list via telephone or the CFPB website.

Prohibits the CFPB from collecting: (1) personally identifiable information about a consumer listed on the opt-out list (except in the case of consumer complaints), or (2) any data or performing any market monitoring unless it has a Senate-confirmed Director.

Prescribes time limitations for the holding of data by the CFPB.

Directs the CFPB, if it experiences a data breach that exposes personally identifiable information about a consumer, to give that consumer one year of free credit monitoring. Requires the CFPB to notify consumers publicly of such a breach on the front page of its website.

Prohibits CFPB employees from accessing personally identifiable information collected by the CFPB unless they hold a "confidential" security clearance.