Cut thin 3-inch round slice from tops of rolls. Remove bread from inside of each roll, leaving 1/2-inch shell on side and bottom. Reserve tops and trimmings for another use.
In 2-quart saucepan, heat cooking sauce, chicken, ham and wild rice to boiling, stirring occasionally. Reduce heat low; simmer 10 minutes to blend flavors, stirring occasionally.
Fill soup bowls one-third full with soup. Place rolls on top of soup. Spoon additional soup into cavity of rolls, allowing some to overflow into bowls. Top each serving with almonds and chives.