Heat the oil in a large, heavy saucepan or Dutch oven over medium-low heat. Add the broken spaghetti, onion, and garlic. Cook, stirring occasionally, until the spaghetti starts to brown, 3-4 minutes.
Puree the 2 cans of undrained tomatoes and chilies in a blender until smooth. Add to the saucepan along with the chicken broth. Cover pan and simmer for 10-15 minutes or until the spaghetti is tender. Season to taste with salt and pepper.