The propagation of the rupture of the M_w7.9 Denali fault earthquake from the central Denali fault onto the Totschunda fault has provided a basis for dynamic models of fault branching in which the angle of the regional or local prestress relative to the orientation of the main fault and branch plays a principal role in determining which fault branch is taken. GeoEarthScope LiDAR and paleoseismic data allow us to map the structure of the Denali-Totschunda fault intersection and evaluate controls of fault branching from a geological perspective. LiDAR data reveal the Denali-Totschunda fault intersection is structurally simple with the two faults directly connected. At the branch point, 227.2 km east of the 2002 epicenter, the 2002 rupture diverges southeast to become the Totschunda fault. We use paleoseismic data to propose that differences in the accumulated strain on each fault segment, which express differences in the elapsed time since the most recent event, was one important control of the branching direction. We suggest that data on event history, slip rate, paleo offsets, fault geometry and structure, and connectivity, especially on high slip rate-short recurrence interval faults, can be used to assess the likelihood of branching and its direction. Analysis of the Denali-Totschunda fault intersection has implications for evaluating the potential for a rupture to propagate across other types of fault intersections and for characterizing sources of future large earthquakes.