Femtosecond lasers with high repetition rates are attractive for spectroscopic applications with high sampling rates, high power per comb line, and resolvable lines. However, at long wavelengths beyond 2 µm, current laser sources are either limited to low output power or repetition rates below 1 GHz. Here we present an ultrafast laser oscillator operating with high output power at multi-GHz repetition rate. The laser produces transform-limited 155-fs pulses at a repetition rate of 2 GHz, and an average power of 0.8 W, reaching up to 0.7 mW per comb line at the center wavelength of 2.38 µm. We have achieved this milestone via a Cr²⁺-doped ZnS solid-state laser modelocked with an InGaSb/GaSb SESAM. The laser is stable over several hours of operation. The integrated relative intensity noise is 0.15% rms for [10 Hz, 100 MHz], and the laser becomes shot noise limited (-160 dBc/Hz) at frequencies above 10 MHz. Our timing jitter measurements reveal contributions from pump laser noise and relaxation oscillations, with a timing jitter of 100 fs integrated over [3 kHz, 100 MHz]. These results open up a path towards fast and sensitive spectroscopy directly above 2 µm.