Although dietary Met, as the first limiting amino acid (AA), has been extensively studied for poultry, little is known about how the supply and source of free Met affect tissue composition. The purpose of this study was to investigate the effect of feeding young broiler chickens with a deficient or sufficient TSAA (Met+Cys) supply, using either dl-Met (dl-Met+ and dl-Met-, for respectively diets sufficient and deficient in TSAA) or dl-2-hydroxy-4-methylthiobutyric acid (HMTBA+ and HMTBA-, for respectively diets sufficient and deficient in TSAA) as a Met source on tissue composition and breast muscle traits. For both Met sources, the deficient diets were formulated to provide true digestible Met:Lys and TSAA:Lys respectively 45% and 30% below that of the sufficient diets. Performance and tissue weights were affected by the Met supply but not by the Met source. In TSAA-deficient chickens, ADG and FCR, and protein content in empty body and pectoralis major muscles (PM) were lower than in TSAA-sufficient chickens (P < 0.05). Reducing the Met content of the diet increased the redness value of PM (a*) and the hue angle (H°; P < 0.01). The source of Met affected body AA composition and the partitioning of body Cys among tissues (P < 0.05). In TSAA-deficient birds, body Cys mass decreased in the commercial carcass and PM, but increased in the rest of the body (P < 0.01). The Met source also had an impact on the Cys mass, which was reduced in the commercial carcass and PM of dl-Met birds, but higher in the rest, especially in the feathers of TSAA-deficient birds (P < 0.05). The Met source, supply, or both altered the AA composition of the empty body, mostly in the commercial carcass. In conclusion, a dietary TSAA deficiency altered performance, tissue composition and quality traits of PM of broilers. There was no impact between dietary dl-Met and dl-HMTBA on performance or muscle weight, although the Met source affected the partitioning of Cys among tissues.