We analyze the physical conditions of the cool, photoionized (T ~104 K) circumgalactic medium (CGM) using the COS-Halos suite of gas column density measurements for 44 gaseous halos within 160 kpc of L ~ L* galaxies at z ~ 0.2. These data are well described by simple photoionization models, with the gas highly ionized (n H II /n H gsim 99%) by the extragalactic ultraviolet background. Scaling by estimates for the virial radius, R vir, we show that the ionization state (tracked by the dimensionless ionization parameter, U) increases with distance from the host galaxy. The ionization parameters imply a decreasing volume density profile n H = (10–4.2 ± 0.25)(R/R vir)–0.8 ± 0.3. Our derived gas volume densities are several orders of magnitude lower than predictions from standard two-phase models with a cool medium in pressure equilibrium with a hot, coronal medium expected in virialized halos at this mass scale. Applying the ionization corrections to the H I column densities, we estimate a lower limit to the cool gas mass $M_{\rm CGM}^{\rm cool} \gt 6.5 \times 10^{10}$ M ☉ for the volume within R < R vir. Allowing for an additional warm-hot, O VI-traced phase, the CGM accounts for at least half of the baryons purported to be missing from dark matter halos at the 1012 M ☉ scale.