We present a systematic study on the effect of surface chemistry on thermal transport in colloidal nanocrystal (NC) solids. Using PbS NCs as a model system, we vary ligand binding group (thiol, amine, and atomic halides), ligand length (ethanedithiol, butanedithiol, hexanedithiol, and octanedithiol), and NC diameter (3.3-8.2 nm). Our experiments reveal several findings: (i) The ligand choice can vary the NC solid thermal conductivity by up to a factor of 2.5. (ii) The ligand binding strength to the NC core does not significantly impact thermal conductivity. (iii) Reducing the ligand length can decrease the interparticle distance, which increases thermal conductivity. (iv) Increasing the NC diameter increases thermal conductivity. (v) The effect of surface chemistry can exceed the effect of NC diameter and becomes more pronounced as NC diameter decreases. By combining these trends, we demonstrate that the thermal conductivity of NC solids can be varied by an overall factor of 4, from ∼0.1-0.4 W/m-K. We complement these findings with effective medium approximation modeling and identify thermal transport in the ligand matrix as the rate-limiter for thermal transport. By combining these modeling results with our experimental observations, we conclude that future efforts to increase thermal conductivity in NC solids should focus on the ligand-ligand interface between neighboring NCs.