No, only by using a cheat device, hacking or trading on GTS or with friends. If you want, you could ask a friend to breed a baby Chespin at the day care in exchange for a baby Froakie or Fennekin. Or just keep trading on the GTS and hope you get lucky.
But as far as I know, you can not gain the third starter Pokémon in the game without the ways I stated above.
EDIT: I think towards the start of the game you battle against Serena who will have a Chespin/Quilladin/Chesnaught on her team