Heat olive oil and butter or margarine in a large skillet over medium heat. Add the potatoes and cook for about 5 minutes, until they just start to brown on one side.
Add the onion and green pepper. Continue cooking until onion is translucent, about another 5 minutes.
Stir in the carrots, chicken and seasonings. Cook, stirring often, until potatoes are tender and browned all over, about 10-15 more minutes.
If desired, serve with chicken gravy (or ketchup!).
Quick Chicken Gravy
Melt butter or margarine over medium heat. Whisk in flour and cook for 2-3 minutes. Whisk in chicken stock, bring to a boil, and simmer until thickened to desired consistency. Stir in pepper and thyme.
Notes
*A great thing about this dish is that the shredded carrots look just like pieces of melted cheese.