The complex formed by U1A RBD1 and the U1 snRNA stem/loop II is noted for its high affinity and exquisite specificity. Here, that complex is investigated by 5 ns molecular dynamics simulations and analyzed by reorientational eigenmode dynamics to determine the dynamic properties of the RNA:protein interface that could contribute to the binding mechanism. The analysis shows that there is extensive correlation between motions of the RNA and protein, involving 7 of the 10 RNA loop nucleotides, the protein β-sheet surface, two of its loops, and its C-terminal tripeptide sequence. Order parameters of these regions of the complex are uniformly high, indicating restricted motion. However, several regions of both RNA and protein retain local flexibility, notably three nucleotides of the RNA loop and one loop of RBD1 that does not contact RNA. The highly correlated motions involving both molecules reflect the intricate network of interactions that characterize this complex and could account in part for the thermodynamic coupling observed for complex formation.