  We show that for a $C^1$ generic vector field $X$ away from homoclinic
tangencies, a nontrivial Lyapunov stable chain recurrence class is a homoclinic
class. The proof uses an argument with $C^2$ vector fields approaching $X$ in
$C^1$ topology, with their Gibbs $F$-states converging to a Gibbs $F$-state of
$X$.
