The chemical evolution of fluorine is investigated in a sample of Milky Way red giant stars that span a significant range in metallicity from [Fe/H] ∼-1.3 to 0.0 dex. Fluorine abundances are derived from vibration-rotation lines of HF in high-resolution infrared spectra near 2.335 μm. The red giants are members of the thin and thick disk/halo, with two stars being likely members of the outer disk Monoceros overdensity. At lower metallicities, with [Fe/H] <-0.4 to-0.5, the abundance of F varies as a primary element with respect to the Fe abundance, with a constant subsolar value of [F/Fe] ∼-0.3 to-0.4 dex. At larger metallicities, however, [F/Fe] increases rapidly with [Fe/H] and displays a near-secondary behavior with respect to Fe. Comparisons with various models of chemical evolution suggest that in the low-metallicity regime (dominated here by thick-disk stars), a primary evolution of 19F with Fe, with a subsolar [F/Fe] value that roughly matches the observed plateau, can be reproduced by a model incorporating neutrino nucleosynthesis in the aftermath of the core collapse in Type II supernovae. A primary behavior for [F/Fe] at low metallicity is also observed for a model including rapidly rotating low-metallicity massive stars, but this overproduces [F/Fe] at low metallicity. The thick-disk red giants in our sample span a large range of galactocentric distance (R g ∼ 6-13.7 kpc) yet display a roughly constant value of [F/Fe], indicating a very flat gradient (with a slope of 0.02 ± 0.03 dex kpc-1) of this elemental ratio over a significant portion of the Galaxy having