This paper reports evidence that learners commonly develop a notion of chemical stability that, whilst drawing upon ideas taught in the curriculum, is nevertheless inconsistent with basic scientific principles. A series of related small-scale studies show that many college-level students consider a chemical species with an octet structure, or a full outer shell, will necessarily be more stable than a related species without such an electronic configuration. Whilst this finding is in itself consistent with previous research, the present paper shows how students commonly apply this criterion without consideration of chemical context, or other significant factors such as net charge. Species that would seem highly unstable and non-viable from chemical considerations, such as Na[superscript 7-], C[superscript 4+] and even Cl[superscript 11-], are commonly judged as being stable. This research shows that many college-level students are privileging a simple heuristic (species with full outer shells will be stable) when asked about the stability of chemical species at the submicroscopic level, to the exclusion of more pertinent considerations. Some students will even judge an atom in an excited state as more stable than when in the ground state, when an electron is promoted from an inner shell to "fill" the outer shell. It is suggested that the apparently widespread adoption of a perspective that is so at odds with the science in the curriculum is highly significant for the teaching of chemistry, and indicates the need for more detailed studies of how such thinking develops and can be challenged. (Contains 13 tables and 7 figures.)