The supercritical water-cooled nuclear reactor (SCWR) concept offers potential for superior economics due to its high thermal efficiency and plant simplification. However, design of a thermal-spectrum core for such a reactor is complicated by the relatively low density of the water coolant and therefore reduced moderation. This requires the SCWR design to include a dedicated moderator. One solution explored worldwide is based on the use of water rods. In this paper we assess the feasibility of a different approach based on solid moderators, which has some potential advantages including increased core thermal capacity, reduced coolant worth, and simplified vessel internals. The neutronic performance of several solid moderators was evaluated and compared to that of water rods. It was found that the only acceptable solid moderator is zirconium hydride. Axial and local peaking can be readily suppressed by modest variations of the enrichment in a manner similar to the boiling water reactor practice. The Doppler and coolant reactivity coefficients are both negative and in the range of light water reactor experience. The use of zirconium hydride as a stable structural core component was evaluated and found to be acceptable under steady-state and accident conditions. In addition to its chemical and mechanical stability, zirconium hydride can also be fabricated with existing technology. However, its impact on the SCWR cost of electricity generation is deemed significant.