Remove top tortilla from plate and place on flat work surface. Keep remaining tortillas stacked between paper towels in microwave until ready to use.
Dollop ¼ cup refried beans onto center of tortilla and spread beans out horizontally, keeping beans in middle of tortilla. Leave approximately 1 to 2 inches between edge of bean layer and edge of tortilla.
Top layer of beans with ½ cup rice, spreading rice out to cover beans evenly.
Top rice with chopped chicken and ¼ cup shredded cheese, spreading each layer of ingredients out evenly. Add any additional toppings as desired.
Gently run fingers under edges of tortilla to ensure tortilla doesn't stick, then carefully lift edge of tortilla farthest from you. Fold edge down and over filling to meet bottom edge of tortilla (edge closest to you). Lightly press on filling, then unfold tortilla. Filling should now mostly cover bottom half of tortilla.
Gently fold left and right edges of tortilla in toward center, covering filling as much as possible without overlapping edges of tortilla. If tortilla edges don't touch, that's fine.
With sides of tortilla folded in, gently lift bottom edge of tortilla (edge closest to you) and fold tortilla up toward center, covering filling. Tuck bottom edge of tortilla under top edge of filling.
Gently but tightly roll tortilla away from you, holding sides together as needed, until burrito is completely rolled. Place rolled burrito seam-side down on large plate and set aside. Repeat process with remaining tortillas, until all 4 burritos have been rolled.
Serve burritos immediately, or warm burritos to melt cheese (optional, see Notes below) and then serve. To freeze burritos for later, see Notes below.