The CMS Binary Chip (CBC) is a front-end ASIC to be used by the CMS tracker following its upgrade for High Luminosity LHC operation. It will instrument special silicon microstrip detectors to identify high transverse momentum particles in real time so tracking data can be used in the L1 trigger. The CBC should be robust against Single Event Upsets (SEUs). SEU rates have been measured in a series of tests in a 62 MeV proton beam. Each version of the chip has increased the digital circuitry, and hence the SEU susceptibility, and has also been subject to design improvements which affect SEU tolerance. The relevant design features are explained and SEU measurements reported. The expected SEU rates at the HL-LHC are estimated.