Poach chicken in broth on a low simmer for about 15 to 20 minutes or until chicken is mostly done. It will finish cooking in the oven. Remove the chicken and set aside to cool but reserve the stock. Preheat the oven to 400 degrees.
In a large Pyrex measuring cup, melt 1/2 stick of butter in the microwave and pour that into the bottom of a 9 x 13 inch baking pan. Shred the chicken and spread it on top of the butter. In that same Pyrex cup, whisk together the milk and the flour and slowly pour that over the chicken taking care not to disturb the chicken too much. Do not stir.
Strain the chicken stock through a colander into the same Pyrex measuring cup and whisk in the cream of chicken soup. Very carefully pour that over the flour and milk mixture and again, do not stir. Bake uncovered at 400 degrees for 35 to 45 minutes, or until top is light golden brown.