A strategy for enriching the meat of slow-growing chickens with n-3 fatty acids from tuna oil (TO) or linseed oil (LO) is proposed. The effects of TO or LO supplementation on the growth performance of the chickens and the quality, cholesterol content, and fatty acid composition of the meat were examined. A total of 560 21-day-old mixed-sex Thai indigenous crossbred chickens was assigned to a completely randomized design with 7 treatment diets and 4 replicates. The control group consumed a basal diet of corn-soybean meal supplemented with rice bran oil (RBO; 6%). In the experimental diets, RBO was replaced with 2, 4, or 6% TO (TO2, TO4, and TO6) or with 2, 4, or 6% LO (LO2, LO4, and LO6). All groups received 6% added oil. The TO6 diet lowered the final BW and FCR. The boiling loss of breast meat was highest in LO6 and differed from the losses in the control and TO2 groups. Meat from TO4 and LO6 yielded the lowest n-6/n-3 ratio. The alpha-linolenic acid (ALA) content linearly increased across the LO group. The n-3 fatty acid accumulation in the slow-growing chickens was nutritionally valuable for human consumption. Breast meat from TO2 and TO4 provided >250 mg docosahexaenoic acid (DHA) per 100 g fresh meat. Thigh meat from at least 2% TO or 6% LO contained >80 mg (eicosapentaenoic acid + DHA)/100 g meat and 600 mg ALA/100 g meat, respectively, reaching the “high in n-3 polyunsaturated fatty acids” threshold in dietary recommendations.