While previous studies have evaluated the change in stability for the addition or removal of individual species from trophic food chains and food webs, we know of no study that presents a general theory for how stability changes with the addition or removal of trophic levels. In this study, we present a simple model of a linear food chain and systematically evaluate how stability-measured as invariability-changes with the addition or removal of trophic levels. We identify the presence of trophic cascades in the stability of species. Owing to top-down control by predation and bottom-up regulation by prey, we find that stability of a species is highest when it is at the top of the food chain and lowest when it is just under the top of the food chain. Thus, stability shows patterns identical to those of mean biomass with the addition or removal of trophic levels in food chains. Our results provide a baseline towards a general theory of the effect of adding or removing trophic levels on stability, which can be used to inform empirical studies.