No fucking way. You guys have Andersen, Hiller AND Gibson who can all be good starters. I'm gonna say trade one of Hiller and Andersen. I'd probably trade Andersen before Hiller because a) Andersen is young and will fetch a better return than Hiller, b) if you keep Andersen you'll run into a Canucks-like goaltender situation where there's no clear Nr. 1 and c) a Veteran goaltender would be a better mentor for Gibson.
Trade Andersen to someone that needs a young goaltender (Edmonton AGAIN :lol, or Pittsburgh, who knows.), have Hiller start the majority of games, but give Gibson like 20-30 games or so, including some important ones, to have him build experience. Then the season after that make Hiller the backup if he's still around or trade him and sign a new backup to Gibson.