A new tracking system is under development for the CMS experiment at the High Luminosity LHC (HL-LHC), located at CERN. It includes a silicon tracker that will correlate clusters in two closely spaced sensor layers, for the rejection of hits from low transverse momentum tracks. This will allow tracker data to be read out to the Level-1 trigger at 40 MHz. The Level-1 track-finder must be able to identify tracks with transverse momentum above 2-3 GeV/c within latency constraints. A concept for an FPGA-based track finder using a fully time-multiplexed architecture is presented, where track candidates are identified using a Hough Transform, and then refined with a Kalman Filter. Both steps are fully implemented in FPGA firmware. A hardware system built from MP7 MicroTCA processing cards has been assembled, which demonstrates a realistic slice of the track finder in order to help gauge the performance and requirements for a final system. Abstract. A new tracking system is under development for the CMS experiment at the High Luminosity LHC (HL-LHC), located at CERN. It includes a silicon tracker that will correlate clusters in two closely spaced sensor layers, for the rejection of hits from low transverse momentum tracks. This will allow tracker data to be read out to the Level-1 trigger at 40 MHz. The Level-1 track-finder must be able to identify tracks with transverse momentum above 2-3 GeV/c within latency constraints. A concept for an FPGA-based track finder using a fully time-multiplexed architecture is presented, where track candidates are identified using a Hough Transform, and then refined with a Kalman Filter. Both steps are fully implemented in FPGA firmware. A hardware system built from MP7 MicroTCA processing cards has been assembled, which demonstrates a realistic slice of the track finder in order to help gauge the performance and requirements for a final system.