Cook broccoli as directed on package. Drain.
Meanwhile, in 4-quart saucepan, melt butter over medium heat. Add celery, carrot, onion and thyme; cook 5 to 7 minutes, stirring occasionally, until vegetables are crisp-tender.
Stir in flour until well blended. Add milk and broth; cook until mixture boils and thickens, stirring constantly.
Stir in chicken and cooked broccoli; simmer about 5 minutes, stirring occasionally, until hot. Add cheese; stir until melted.