If using a whole chicken, boil it in a big pot of water until cooked through and falling apart.
Save the pot of chicken water, remove the chicken, and cook the spaghetti noodles in the broth according to package directions. (If using rotisserie chicken, just add a touch of chicken bouillon to a pot of water before boiling the pasta).
Shred the chicken meat and set it aside, discarding the bones.
Drain the pasta, return the empty pot to the stove over medium heat, and add a drizzle of oil.
Cook the chopped onion and celery, stirring often, until softened.
Add the cubed Velveeta, Rotel, and cream of mushroom soup to the vegetables.
Stir continuously until all the cheese is completely melted into a smooth sauce.
Add the cooked pasta and shredded chicken back to the pot, tossing well to coat.
Season with 1 to 2 teaspoons of Cajun seasoning to taste. Notes:
Do not drain the Rotel tomatoes before adding them to the pot; the juices add great flavor.
If leftovers are a little dry, simply add a little bit of milk when reheating and it will be perfectly creamy again