The thermal stability of GaAs(C)/InAs superlattices grown by metalorganic molecular beam epitaxy on InP substrates has been examined by Hall measurements, transmission electron microscopy, and high resolution x-ray diffraction. These structures provide an ordered counterpart to a random In0.53Ga0.47As alloy, in which high concentration carbon doping is generally difficult to achieve. In a 43 period (23 angstrom GaAs/26 angstrom InAs) superlattice in which the GaAs was C-doped and the InAs undoped an average hole concentration of 7 X 10(19) cm-3 and hole mobility of 20 cm2 V-1 s-1 was achieved. Such structures are stable against rapid thermal annealing (10 s) up to 750-degrees-C. An 850-degrees-C/10 s anneal reduced the hole concentration to 1.5 X 10(19) cm-3, accompanied by the onset of intermixing of the superlattice. The surface morphology of all but very thick (36 angstrom GaAs/40 angstrom InAs) period superlattice structures remained specular, even after 850-degrees-C, 10 s annealing. These superlattices show properties suitable for use in a range of electronic and photonic devices, particularly InP-based lasers and heterojunction bipolar transistors.