Increasing evidence suggests that the mechanism(s) for heating the chromospheres of the coolest red giants may be quite different from those responsible for heating in solar-type stars, but little progress toward a quantitative test of this important idea has been made, both because of the scarcity of suitable observations and the difficulty of creating NLTE model chromospheres. We report here the results of NLTE calculations for 10 “classical” model chromospheres (differing mainly in the column mass density above the temperature minimum) and one “shock” chromosphere for a cool giant star and compare the results to observations of 30 g Her (M6 III), one of the coolest (Teff = 3250 K) SRb (semi-regular) variable stars. Observed chromospheric spectral features include Mg II h & k; C II] UV0.01; Mg I λ2852; Ca II H, K & IRT; Ca I λ4227 & λ6573; Al II] UV1; and Balmer α. The equations of statistical equilibrium and radiative transfer are solved self-consistently for H I, H-, H2, He I, C I, C II, Na I, Mg I, Mg II, Al I, Al II, Ca I, and Ca II with the equivalent two-level-atom technique in a one-dimensional, hydrostatic, plane-parallel atmosphere. Synthetic spectra from the classical models are compared in detail with observations of 30 g Her. However, we find that no single-component classical model in hydrostatic equilibrium is able to reproduce both the Mg II line profiles and the relative strengths of the C II] lines. Some non-classical feature — either departures from hydrostatic equilibrium, shocks, inhomogeneities, or unusual velocity fields — is called for. Surprisingly, however, synthetic spectra from our simple shock model reproduce both of these ionic multiplets, but only if we severely constrain the temperature and thickness of the chromosphere and the position of a shock between the chromosphere and photosphere.