A new method was developed to 3D print high-thermal-conductivity, pitch-based continuous carbon fiber composites. This process uses a dual extruder to selectively print polylactic acid (PLA) or PLA-coated pitch carbon fibers. The effective thermal conductivity of unidirectionally 3D-printed specimens was characterized experimentally for samples fabricated from fibers with different conductivities and at different volume fractions: Three grades of pitch carbon fibers were used with conductivities ranging from 140 to 800 W/mK. Carbon fiber volume fractions ranging from 6.25% to 11.7% were investigated. A maximum thermal effective thermal conductivity of 37.1 W/mK was measured for a 9.5% volume fraction of the K13D2U pitch carbon fiber which is significantly higher than that of any 3D-printed carbon-based composites measured previously. However, the measured effective thermal conductivities were significantly lower than those predicted by the parallel model. Breakage of the fibers post-printing was confirmed using micro-computed tomography and suggests that higher effective thermal conductivities can be obtained by better mitigating fiber breakage during the printing process. Future directions for this technology are discussed.