Theoretical models and spectroscopic observations of newborn stars suggest that protoplantary disks have an inner "wall" at a distance set by the disk interaction with the star. Around T Tauri stars, the size of this disk hole is expected to be on a 0.1-AU scale that is unresolved by current adaptive optics imaging, though some model-dependent constraints have been obtained by near-infrared interferometry. Here we report the first measurement of the inner disk wall around a solar-mass young stellar object, YLW 16B in the {ρ} Ophiuchi star-forming region, by detecting the light travel time of the variable radiation from the stellar surface to the disk. Consistent time lags were detected on two nights, when the time series in H (1.6 {μ}m) and K (2.2 {μ}m) bands were synchronized while the 4.5 {μ}m emission lagged by 74.5 +/- 3.2 seconds. Considering the nearly edge-on geometry of the disk, the inner rim should be 0.084 AU from the protostar on average, with an error of order 0.01 AU. This size is likely larger than the range of magnetospheric truncations, and consistent with an optically and geometrically thick disk front at the dust sublimation radius at ~1500 K. The widths of the cross-correlation functions between the data in different wavebands place possible new constraints on the geometry of the disk. ; Comment: 23 pages, 9 figures, 2 tables, Accepted for publication in the Astrophysical Journal