About half of the 8 cm/yr of oblique convergence across the active convergent plate boundaries of Taiwan occurs in eastern Taiwan, across the Longitudinal Valley. Significant shortening and left‐lateral slip occurs across the Longitudinal Valley fault there, both as shallow fault creep and as seismogenic fault slip. The southernmost Longitudinal Valley fault comprises an eastern Peinan strand and a western Luyeh strand. We derive an interseismic block model for these two strands using data from a small‐aperture Global Positioning System (GPS) campaign and leveling. The model provides estimates of fault slip rates and quantifies slip partitioning between the two strands. A 45 mm/yr dip‐slip rate on the northern Peinan strand diminishes southward, whereas the left‐lateral component increases. In contrast, nearly pure dip‐slip motion of about 20 mm/yr on the southern Luyeh strand diminishes northward to about 8 mm/yr and picks up a component of left‐lateral motion of about 15 mm/yr before it dies out altogether at its northern terminus. The Luyeh and the northern Peinan strands record near‐surface creep, but the southern Peinan strand appears locked. The potential earthquake magnitude for the two strands may be as high as Mw 6.5. We anticipate seismic rupture mainly on the locked portion of the Peinan strand.