We demonstrate a technique for differential coherent anti-Stokes Raman scattering (CARS) microscopy employing linearly chirped femtosecond laser pulses. By replicating the exciting pump-Stokes pulse pairs to create a pulse train at twice the laser repetition rate, and controlling the instantaneous frequency difference of each pair by glass dispersion, we can adjust the Raman frequency probed by each pair in an intrinsically stable and cost-effective way. The resulting CARS intensities are detected by a single photomultiplier as sum and difference using phase-sensitive frequency filtering. We demonstrate imaging of polymer beads and living cells with suppressed nonresonant CARS background and improved chemical sensitivity.