I've read that it's only possible if the female is the St. Bernard. She's large enough to produce live offspring. But a female chihuahua, assuming she somehow survives an encounter with a male St. Bernard, isn't be large enough to drop the resulting litter. Otherwise, I think that at the genetic level the mating is no problem at all.
Very interesting.
I wonder what the pups resulting from such a union would look like.
St. Barnard - Chihuahua: A ring species in the making.