Tantalum carbides are commonly processed by hot pressing, canned hot-isostatic-pressing, or spark plasma sintering because of their high melting temperatures and low diffusivities. This paper reports processing of dense -Ta4C3-x by reaction sintering of a Ta and TaC powder mixture (C/Ta atomic ratio = 0.66). -Ta4C3-x is of interest due to its rhombohedral (trigonal) crystal structure that may be characterized as a polytype with both face-centered-cubic and hexagonal-close-packed Ta stacking sequences interrupted by stacking faults and missing carbon layers. This structure leads to easy cleaving on the basal planes and high fracture toughness. A key step in processing is the hydrogenation of the Ta powder to produce -TaHx, a hard and brittle phase that enables efficient comminution during milling and production of small, equiaxed Ta particles that can be packed to high green density with the TaC powder. Studies of phase evolution by quantitative X-ray diffraction during sintering revealed several intermediate reactions: (1) decomposition of -TaHx to Ta; (2) diffusion of C from -TaC to Ta leading to the formation of -Ta2Cy' with the kinetics described by the Avrami equation with an exponent, n=0.5, and an activation energy of 219kJ/mole; (3) equilibration of -Ta2Cy' and -TaC0.78 phases; and (4) formation of -Ta4C2.56 from the equilibrated -Ta2C and -TaC0.78 phases with the kinetics characterized by a higher Avrami exponent (n approximate to 3) and higher activation energy (1007kJ/mole). The sintered material contained similar to 0.86 weight fraction -Ta4C2.56 and similar to 0.14 weight fraction -TaC0.78 phases. The microstructure showed evidence of nucleation and growth of the -Ta4C2.56 phase in both the -Ta2C and -TaC0.78 parent phases with distinct difference in the morphology due to the different number of variants of the habit plane.