In a food processor or blender, combine olive oil, lemon juice, garlic, basil, walnuts, salt, and pepper for the pesto. Add more lemon juice, salt, and/or pepper to taste.
Arrange the chicken in the bottom of a large slow cooker. (You can use frozen.)
Top with cheese, then pour the pesto evenly over top. Cover with a layer of foil or parchment paper.
Scrub sweet potatoes well (leaving the skin on), prick with a fork, and lay them on top of the paper or foil. Cover and cook on low for 6-7 hours or on high for 4-5 hours. (If your chicken is frozen it will take a bit longer.)
Use tongs to carefully remove the sweet potatoes as well as the foil or parchment. The steam that comes out will be quite hot; keep small children away!
Serve chicken and sweet potatoes alongside a salad of greens and orange wedges, topped with your favorite dressing.