Place the chicken, taco seasoning and cream cheese in the slow cooker and cook on LOW for 6-8 hours. During the final hour, stir together, break-up/shred the chicken and stir in the beans and lime juice. Continue cooking until heated through.
To serve, place about 3/4 - 1 cup of the chicken mixture into the center of a tortilla and top with about 1/4 cup of the shredded Monterey Jack cheese. Fold to seal in the filling.
Heat about a tablespoon of oil in a large, non-stick pan over medium heat (I was able to cook three chimichangas at once in mine).
Turn the chimichangas to coat lightly in oil. Cook, starting with the seam side down, until all sides are nicely browned and the cheese inside is melted.
Serve immediately.