We present the high-resolution Chandra X-ray Observatory persistent (non-dip) spectrum of 4U 1916-05 which revealed narrow absorption lines from hydrogenic neon, magnesium, silicon, and sulfur, in addition to the previous identified hydrogenic and helium-like iron absorption lines. This makes 4U 1916-05 only the second of the classical X-ray dipper systems to show narrow absorption lines from elements other than iron. We propose two possible explanations for the small measured line widths (>~ 500-2000 km s^{-1}), compared to the expected Keplerian velocities (> 1000 km s^{-1}) of the accretion disk in this 50-min orbital period system, and lack of wavelength shifts (>~ 250 km s^{-1}). First, the ionized absorber may be stationary. Alternatively, the line properties may measure the relative size of the emission region. From this hypothesis, we find that the emission region is constrained to be >~ 0.25 times the radial extent of the absorber. Our results also imply that the ionized absorber spans a range of ionization parameters.
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