In Cre site-specific recombination, the synaptic intermediate is a recombinase homotetramer containing a pair of DNA target sites. The strand-exchange mechanism proceeds via a Holliday-junction (HJ) intermediate; however, the geometry of the DNA segments in the synapse has remained highly controversial. In particular, all crystallographic structures are consistent with an achiral planar Holliday-junction (HJ) structure, whereas topological assays based on Cre-mediated knotting of plasmid DNAs are consistent with a right-handed chiral junction. Here we use the kinetics of loop closure involving closely spaced (131-151 bp), directly repeated loxP sites to investigate the in-aqueo ensemble of conformations for the longest-lived looped DNA intermediate. Fitting the experimental site-spacing dependence of the loop-closure probability, J, to a statistical-mechanical theory of DNA looping provides evidence for substantial out-ofplane HJ distortion. This result unequivocally stands in contrast to the square-planar intermediate geometry determined from crystallographic data for the Cre-loxP system and other int-superfamily recombinases. J measurements carried out with an isomerization-deficient Cre mutant suggest that the apparent geometry of the wild-type complex may result from the temporal averaging of diverse right-handed and achiral structures. Applied to Cre recombinase, and other biological systems, our approach bridges the static pictures provided by crystal structures and the natural dynamics of macromolecules in vivo. This approach thus advances a more comprehensive dynamic analysis of large nucleoprotein structures and their mechanisms.