This paper deals with chain graphs under the classic
Lauritzen-Wermuth-Frydenberg interpretation. We prove that the regular Gaussian
distributions that factorize with respect to a chain graph $G$ with $d$
parameters have positive Lebesgue measure with respect to $\mathbb{R}^d$,
whereas those that factorize with respect to $G$ but are not faithful to it
have zero Lebesgue measure with respect to $\mathbb{R}^d$. This means that, in
the measure-theoretic sense described, almost all the regular Gaussian
distributions that factorize with respect to $G$ are faithful to it.