The importance of loop structures in the corona, both for flares and for the quiet Sun, has stimulated considerable attention to questions of their thermal stability. Previous studies have focused attention on the coronal part of the loop. In this paper we examine loop stability by treating the entire observable loop, from its photospheric footpoints to its coronal apex. This approach allows the chromosphere and corona to interact naturally, thus avoiding possibly artificial boundary conditions imposed at transition region footpoints.We develop a numerical eigenfunction method for the study of stability, which is based on the methods discussed in a previous paper. For exemplary purposes, we have applied these methods to several loop models based on semiempirical model chromospheres, under the assumption that the rate of ambient energy input per unit mass of plasma depends only on column depth. Our principal study is of a loop model based on the semiempirical model F of Vernazza, Avrett, and Loeser. We find that this loop model has one unstable eigenmode, with a growth time of 2 minutes. This mode appears in the transition region, centered on the peak of the optically thin radiative loss function at T ≈ 105 K. However, we provide evidence that suggests that this instability may not be a feature of real loops. More importantly, we find that (1) this atmosphere is stable to the hydrogen-induced radiative instability of optically thin gases at temperatures around 104.3 K; (2) were it not for radiative transfer effects, this atmosphere would be dramatically unstable, with growth times in the range 1 ≤ r ≤ 18 s; and (3) the stability when radiative transfer is taken into account can be understood primarily as a result of the reduction of the peak in the radiative loss rate at 104.3 K, due to hydrogen, that would exist if the chromosphere were optically thin. This reduction is due to the significant optical depth, and consequent low escape probability, of radiation of the dominant coolant, Lyα, at upper temperatures.