Place chicken breasts, celery, carrot, onion, and bay leaf in a medium pot and cover with cold water. Bring to a boil, then reduce heat and simmer, covered, for 10 to 12 minutes. Set chicken breasts aside to cool, discarding liquid and vegetables (or save to use as the basis for stock). When chicken is cool enough to handle, dice into ¾″ cubes.
Heat butter and oil in a large skillet and