Background: The qualitative properties of the meat are of major importance for poultry breeding, since meat is now widely consumed as cuts or as processed products. The aim of this study was to evaluate the genetic parameters of several breast meat quality traits and their genetic relationships with muscle characteristics in a heavy commercial line of broilers. Results: Significant levels of heritability (averaging 0.3) were obtained for breast meat quality traits such as pH at 15 min post-slaughter, ultimate pH (pHu), color assessed by lightness L*, redness a* and yellowness b*, drip loss, thawing-cooking loss and shear-force. The rate of decrease in pH early post-mortem and the final pH of the meat were shown to be key factors of chicken meat quality. In particular, a decrease in the final pH led to paler, more exudative and tougher breast meat. The level of glycogen stored in breast muscle estimated by the Glycolytic Potential (GP) at slaughter time was shown to be highly heritable (h(2) 0.43). There was a very strong negative genetic correlation (rg) with ultimate meat pH (rg-0.97), suggesting a common genetic control for GP and pHu. While breast muscle weight was genetically positively correlated with fiber size (rg 0.76), it was negatively correlated with the level of glycogen stored in the muscle (rg -0.58), and as a consequence it was positively correlated with the final pH of the meat (rg 0.84). Conclusion: This genetic study confirmed that selection should be useful to improve meat characteristics of meat-type chickens without impairing profitability because no genetic conflict was detected between meat quality and meat quantity. Moreover, the results suggested relevant selection criteria such as ultimate pH, which is strongly related to color, water-holding capacity and texture of the meat in this heavy chicken line.