This is the first report providing estimates of the genetic basis of breast muscle myopathies (BMM) and their relationship with growth and yield in broiler chickens. In addition, this paper addresses the hypothesis that genetic selection for increase breast yield has contributed to the onset of BMM. Data were analyzed from ongoing recording of BMM within the Aviagen breeding program. This study focused on three BMM: deep pectoral myopathy (DPM; binary trait), white striping (WS; 4 categories) and wooden breast (WB; 3 categories). Data from two purebred commercial broiler lines (A and B) were utilized providing greater than 40,000 meat quality records per line. The difference in selection history between these two lines has resulted in contrasting breast yield (BY): 29% for Line A and 21% for Line B. Data were analyzed to estimate genetic parameters using a multivariate animal model including six traits: body weight (BW), processing body weight (PW), BY, DPM, WB, and WS, in addition to the appropriate fixed effects and permanent environmental effect of the dam. Results indicate similar patterns of heritability and genetic correlations for the two lines. Heritabilities (h 2) of BW, PW and BY ranged from 0.271–0.418; for DPM and WB h 2 <0.1; and for WS h 2 ≤0.338. Genetic correlations between the BMM and BW, PW, or BY were ≤0.132 in Line A and ≤0.248 in Line B. This paper demonstrates the polygenic nature of these traits and the low genetic relationships with BW, PW, and BY, which facilitates genetic improvement across all traits in a balanced breeding program. It also highlights the importance of understanding the environmental and/or management factors that contribute greater than 65% of the variance in the incidence of white striping of breast muscle and more than 90% of the variance of the incidence of wooden breast and deep pectoral myopathy in broiler chickens.