As a test of rotationally-induced mixing causing the well-known Li dip in older mid-F dwarfs in the local Galactic disk, we utilize high-resolution and-signal-to-noise ratio (S/N) Keck/HIRES spectroscopy to measure the Li abundance in the components of the∼ 1 Gyr,[Fe/H]=-0.15 eclipsing short-period binary V505 Per. We find A (Li)∼ 2.7±0.1 and 2.4±0.2 in the T eff∼ 6500 and 6450 K primary and secondary components, respectively. Previous T eff determinations and uncertainties suggest that each component is located in the midst of the Li dip. If so, their A (Li) are≥ 2–5 times larger than A (Li) detections and upper limits observed in the similar metallicity and intermediate-age open clusters NGC 752 and 3680, as well as the more metal-rich and younger Hyades and Praesepe. These differences are even larger if the consistent estimates of the scaling of initial Li with metallicity inferred from nearby disk stars, open clusters, and recent Galactic chemical evolution models are correct. Our results suggest, independently of complementary evidence based on Li/Be ratios, Be/B ratios, and Li in subgiants evolving out of the Li dip, that main-sequence angular momentum evolution is the origin of the Li dip. Specifically, our stars' A (Li) indicates that tidal synchronization can be sufficiently efficient and occur early enough in short-period binary mid-F stars to reduce the effects of rotationally-induced mixing and destruction of Li occurring during the main-sequence in otherwise similar stars that are not short-period tidally-locked binaries.