Mix the cinnamon, nutmeg, ginger, allspice, paprika, brown sugar, salt and pepper in a small bowl until well combined.
Pat the chicken breasts dry with paper towels, brush them with olive oil, then rub the pumpkin spice mixture all over both sides.
Leave the chicken to marinate for 30 minutes at room temperature while the grill heats up.
Heat the grill or grill pan over medium-high heat. Place the chicken on the grill and cook for 6–7 minutes per side, until the grill marks are dark and an instant-read thermometer reads 74°C (165°F) in the thickest part.
Transfer the chicken to a board and rest for 5 minutes before slicing — this keeps the juices in the meat.
Slice against the grain and serve with cinnamon sticks and a small pumpkin on the side, if you like.
Notes
Marinate 30 minutes before grilling. Rest 5 minutes before slicing. Cook to 74°C (165°F). Total time excludes the 30-minute marinade. Keeps 3 days refrigerated.