Melt butter in a 6 quart pot over medium-high heat.
Add celery, carrots, and onions. Saute until tender crisp.
Stir in flour and mixture will become lumpy.
Add chicken broth and milk. Stir until the lumps are gone.
Cook over medium-high heat, stirring constantly, until it starts to thicken.
Add chicken, ham and cooked wild rice.
Continue heating, stirring often as the soup thickens, until it starts to boil and the chicken, ham and wild rice are hot.
Taste to see if you need to add salt and more pepper. (I added 1 tsp of salt and another 1/2 tsp of pepper.)