Rinse chicken breasts with cold water, pat dry. Cut each breast in half, then quarter. Slice each quarter into thin, 1/2 inch medallions, season with salt and pepper.
In Dutch oven, medium high, heat olive oil and add a few chicken medallions, some diced onions, celery and green peppers. Saute until done, about 5 minutes, then remove and set aside. Keep adding until all chicken is cooked.
Start water in another large pan to boil for spaghetti. Once water boils, add a pinch of salt. Snap spaghetti in half, add to boiling water. Cook until done, stirring occasionally to keep pasta from sticking to bottom of pan (around 10 to 12 minutes).
Meanwhile to pan drippings, add can mushroom soup, Velvetta chunks, low fat milk and stir with medium heat until cheese is melted, sauce is smooth. Add cooked chicken and reduce heat to simmer.
Rinse spaghetti and drain well. Place in serving bowl. Spoon cheesy chicken sauce mixture over spaghetti and serve.