Supplementation of broiler chicken diets with resin rich in bioactive components, such as different boswellic acids, could improve productivity, chemical composition, and nutritive value of produced meat. The aim of the study was to assess the effect of different levels of Boswellia serrata (BSR) supplementation in broiler chicken diet on the basic chemical composition and the Ca, P, Mg, Fe, Zn, and Cu contents in the breast and drumstick muscles and liver. The analyses involved 200 Ross 308 chickens. The broiler chickens were fed with diets containing 0 (BSR0), 1.5 (BSR1.5), 2 (BSR2), and 2.5% (BSR2.5) of B. serrata resin. The supplementation of broiler chicken diets with 2.5% (BSR2.5) decreased linearly the ether extract in breast and drumstick muscles and the calorific value in drumstick muscles (P < 0.05). An increased level of Ca in the breast and drumstick muscles (control vs. BSR diets, linear, P < 0.05) and in the liver (control vs. BSR diets, quadratic, P < 0.05) as well as Mg in the drumstick muscles and liver (control vs. BSR diets, linear, P < 0.05) was noted in the BSR2 and BSR2.5 chicken groups. The BSR supplementation reduced Cu (in the breast and drumstick muscles and liver) (P < 0.05) and Zn retention (in the drumstick muscles) (C vs. BSR, linear, P < 0.05). B. serrata resin can be considered a good feed additive with a positive impact on the dietary value of poultry meat.