Rub chicken with blackened seasoning. Grill over direct medium heat until cooked through and temperature is at least 160°F. Remove from grill and let rest 5 minutes. Dice into 1/2-inch pieces.
Heat oil in a medium stockpot. Add onion and celery and sauté for 3 minutes. Add sweet potatoes, chicken broth and spices; simmer for about 10 minutes until potatoes are just tender. Add chicken, black beans, corn and cream. Simmer 10 minutes.
Serve 1-1/2 cup portions. Garnish with fresh herbs, if desired.