Preheat oven to 350 degrees.
Cook chicken with 1 teaspoon salt and ½ teaspoon pepper in enough water to just cover until done.
Remove from broth, cool, debone and cube; set aside.
Bring broth to a boil and add all of spaghetti and cook until done.
In a medium skillet, saute onion in butter until softened.
Add garlic and saute for an additional minute.
Whisk in Rotel tomatoes, Green Chiles, evaporated milk and cream cheese. Continue stirring until cream cheese is melted and combined.
Once melted and combined, remove sauce from heat and stir in 2 cups of sharp cheddar, a small handful at a time, stirring well between additions to incorporate.
Immediately add to cooked spaghetti mixture.
Gently fold in cooked and cubed chicken.
Pour into a greased casserole dish. Cover with remaining 1 cup grated sharp cheddar cheese and bake at 350 degrees for about 30 minutes or until hot and bubbly.