  Aims. We investigate the effect of chemistry on the stability of starless
cores against gravitational collapse.
  Methods. We combine chemical and radiative transfer simulations in the
context of a modified Bonnor-Ebert sphere to model the effect of chemistry on
the gas temperature, and study the effect of temperature changes on core
stability.
  Results. We find that chemistry has in general very little effect on the
nondimensional radius $\xi_{\rm out}$ which parametrizes the core stability.
Cores that are initially stable or unstable tend to stay near their initial
states, in terms of stability (i.e., $\xi_{\rm out} \sim$ constant), as the
chemistry develops. This result is independent of the initial conditions. We
can however find solutions where $\xi_{\rm out}$ decreases at late times ($t
\gtrsim 10^6 \, \rm yr$) which correspond to increased stabilization caused by
the chemistry. Even though the core stability is unchanged by the chemistry in
most of the models considered here, we cannot rule out the possibility that a
core can evolve from an unstable to a stable state owing to chemical evolution.
The reverse case, where an initially stable core becomes ultimately unstable,
seems highly unlikely.
  Conclusions. Our results indicate that chemistry should be properly accounted
for in studies of star-forming regions, and that further investigations of core
stability especially with hydrodynamical models are warranted.
