Hierarchical assembly models predict a population of supermassive black hole (SMBH) binaries. These are not resolvable by direct imaging but may be detectable via periodic variability (or nanohertz frequency gravitational waves). Following our detection of a 5.2 year periodic signal in the quasar PG 1302-102 (Graham et al. 2015), we present a novel analysis of the optical variability of 243,500 known spectroscopically confirmed quasars using data from the Catalina Real-time Transient Survey (CRTS) to look for close (< 0.1 pc) SMBH systems. Looking for a strong Keplerian periodic signal with at least 1.5 cycles over a baseline of nine years, we find a sample of 111 candidate objects. This is in conservative agreement with theoretical predictions from models of binary SMBH populations. Simulated data sets, assuming stochastic variability, also produce no equivalent candidates implying a low likelihood of spurious detections. The periodicity seen is likely attributable to either jet precession, warped accretion disks or periodic accretion associated with a close SMBH binary system. We also consider how other SMBH binary candidates in the literature appear in CRTS data and show that none of these are equivalent to the identified objects. Finally, the distribution of objects found is consistent with that expected from a gravitational wave-driven population. This implies that circumbinary gas is present at small orbital radii and is being perturbed by the black holes. None of the sources is expected to merge within at least the next century. This study opens a new unique window to study a population of close SMBH binaries that must exist according to our current understanding of galaxy and SMBH evolution.