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 alpha in polybutadiene. Using alpha, 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.