We demonstrate a chirped-pulse Ti:sapphire laser oscillator with both Kerr-lens and semiconductor- saturable-absorber-mirror-assisted mode locking generating 1.1 microJ pulses at 1 MHz pulse repetition rate. The pulses are coupled out of the laser cavity by means of an acousto-optical cavity dumper, have a spectral width that supports a Fourier limit of 74 fs, and currently have a chirped-pulse duration of 5 ps. After compressing the pulses, this laser will be an ideal tool for efficient high-harmonic generation directly from a laser oscillator.