We present the first dual-modelocked femtosecond oscillator operating beyond 2 µm wavelength. This new class of laser is based on a Cr:ZnS gain medium, an InGaSb SESAM for modelocking, and a two-surface reflective device for spatial duplexing of the two modelocked pulse trains (combs). The laser operates at 2.36 µm, and for each comb, we have achieved a FWHM spectral bandwidth of 30 nm, an average power of over 200 mW, and a pulse duration close to 200 fs. The nominal repetition rate is 242 MHz with a sufficiently large repetition rate difference of 4.17 kHz. We also found that the laser is able to produce stable modelocked pulses over a wide range of output powers. This result represents a significant step towards realizing dual-comb applications directly above 2 µm using a single free-running laser.