The content of omega-3 long-chain polyunsaturated fatty acids (n−3 LCPUFA) in chicken meat can be boosted by feeding broilers a diet containing α-linolenic acid (ALA, from flaxseed oil), some of which is converted by hepatic enzymes to n−3 LCPUFA. However, most of the accumulated n−3 polyunsaturated fatty acid (PUFA) in meat tissues is still in the form of ALA. Despite this, the levels of chicken diets are being enhanced by the inclusion of vegetable and marine sources of omega-3 fats. This study investigated whether the capacity of chicken for n−3 LCPUFA accumulation could be enhanced or inhibited by exposure to an increased supply of ALA or n−3 LCPUFA in ovo. Breeder hens were fed either flaxseed oil (High-ALA), fish oil (high n−3 LCPUFA) or tallow- (low n−3 PUFA, Control) based diets. The newly hatched chicks in each group were fed either the High-ALA or the Control diets until harvest at 42 days’ post-hatch. The n−3 PUFA content of egg yolk and day-old chick meat closely matched the n−3 PUFA composition of the maternal diet. In contrast, the n−3 PUFA composition of breast and leg meat tissues of the 42-day-old offspring closely matched the diet fed post-hatch, with no significant effect of maternal diet. Indeed, there was an inhibition of n−3 LCPUFA accumulation in meat of the broilers from the maternal Fish-Oil diet group when fed the post-hatch High-ALA diet. Therefore, this approach is not valid to elevate n-3 LCPUFA in chicken meat.