We demonstrate a simple method for spectral broadening and compression of laser pulses at megahertz repetition rates by self-phase modulation in a large mode area (LMA) fiber. In order to avoid the currently limiting factor of damage by self-focusing, we positively chirp the input pulse, which allows coupling of significantly more energy into the fiber, while maintaining the same spectral bandwidth and compression as compared to the Fourier-limited case at lower energy. Using a commercial chirped pulse Ti:Sa oscillator (Femtolasers, Femtosource XL) with 55fs, 400nJ pulses at 5MHz and an LMA fiber with 25m core diameter, we generate 16fs, 350nJ pulses, which is a factor of 4 more energy than possible with unchirped input pulses. Good stability has been measured over at least 1 hour for the chirped case and unchirped case. Furthermore, with a 5m core diameter LMA fiber we generated compressed pulses with 6fs and 18nJ output energy. This would allow a carrier-to-envelope phase stabilization of the laser system by external selfstabilization via acoustic difference-frequency modulation. The compact size and its simplicity makes the combination of a chirped pulse oscillator with chirped-fiber-broadening an attractive option for ultrafast spectroscopy at MHz repetition rate.