We present a refined orbital solution for the components A, B, and C of the nearby late-M type multiple system LHS 1070. By combining astrometric datapoints from NACO/VLT, CIAO/SUBARU, and PUEO/CFHT, as well as a radial velocity measurement from the newly commissioned near infrared high-resolution spectrograph CRIRES/VLT, we achieve a very precise orbital solution for the B and C components and a first realistic constraint on the much longer orbit of the A-BC system. Both orbits appear to be co-planar. Masses for the B and C components calculated from the new orbital solution (M(B+C) = 0.157 +/- 0.009 M(circle dot)) are in excellent agreement with theoretical models, but do not match empirical mass-luminosity tracks. The preliminary orbit of the A-BC system reveals no mass excess for the A component, giving no indication for a previously proposed fourth (D) component in LHS 1070.