Korat chicken (KRC) is a slow-growing chicken bred in Thailand, whose meat exhibits a unique toughness. A previous study produced KRC breast meat containing high carnosine content through dietary supplementation with β-alanine or L-histidine; however, the KRC that were fed an L-histidine-supplemented diet produced meat that was significantly more tender. Herein, we performed RNA-Seq to identify candidate genes involved in the regulation of carnosine content and meat toughness. Total RNA was isolated from five female KRC breast muscles in each treatment group that KRC fed diets without supplementation, supplemented with β-alanine or L-histidine. Compared to the non-supplemented group, we identified 118 and 198 differentially expressed genes (DEGs) in the β-alanine or L-histidine supplementation groups, respectively. Genes potentially related to meat tenderness—i.e., those regulating myosin, collagen, intramuscular fat, and calpain—were upregulated (LOC107051274, ACSBG1, and CAPNS2) and downregulated (MYO7B, MYBPH, SERPINH1, and PGAM1). However, carnosine synthase gene was not identified. Functional enrichment analysis identified pathways affected by dietary supplementation, including the insulin signaling pathway (β-alanine supplementation) and the insulin resistance and adipocytokine signaling pathways (L-histidine supplementation). The FoxO signaling pathway was identified as a regulatory network for both supplementation groups. The identified genes can be used as molecular markers of meat tenderness in slow-growing chickens.