Combine the chicken stock, potatoes, Velveeta, onion, celery, salt and pepper in a large pot. Bring to a gentle boil. Reduce heat to medium-low; cover and simmer until the potatoes are tender, about 30 minutes.
If you would like your soup thicker, wisk together 1/2 to 3/4 cup of milk and 4 tablespoons of flour making sure there are no lumps. Bring the soup back up to a gentle boil and add the milk/flour mixture and stir to thicken. Reduce heat to medium/low again. Add sour cream at the end before eating letting it simmer long enough for the sour cream to get hot.