Classic experiments show that polybutadiene oligomers align in a network of stretched chains. Furthermore, the oligomers orient almost as strongly as the network, which suggests a large nematic coupling, despite polybutadiene being a flexible polymer. Here, we combine self-consistent field theory (SCFT) and atomistic molecular dynamics (MD) simulations of polymer chains under tension to obtain the nematic coupling constant α in polybutadiene. Using α, we compute the ratio of orientation of free chains and stretched chains of polybutadiene in a melt of stretched chains. We show that nematic coupling in polybutadiene, though not quite enough to induce a nematic phase, is surprisingly strong. When extrapolated to the experimental temperature, we find an orientation ratio of 0.8, consistent with the experimental value of 0.9.