The Large Hadron Collider (LHC) at CERN will undergo major upgrades to increase the instantaneous luminosity up to 5-7.5 x 1034 cm-2s-1. This High Luminosity upgrade of the LHC (HL-LHC) will deliver a total of 3000-4000 fb-1 of proton-proton collisions at a center-of-mass energy of 13-14 TeV. To cope with these challenging environmental conditions, the strip tracker of the CMS experiment will be upgraded using modules with two closely-spaced silicon sensors to provide information to include tracking in the Level-1 trigger selection. This paper describes the performance, in a test beam experiment, of the first prototype module based on the final version of the CMS Binary Chip front-end ASIC before and after the module was irradiated with neutrons. Results demonstrate that the prototype module satisfies the requirements, providing efficient tracking information, after being irradiated with a total fluence comparable to the one expected through the lifetime of the experiment.