Preheat oven to 375°F with rack set in middle position.
Pierce each sweet potato several times with a fork then wrap each individually with foil. Set potatoes directly on racks and bake until fork tender, 45 to 60 minutes.
Meanwhile, line a baking sheet with parchment paper and coat with cooking spray. Pat chicken breasts dry and transfer to baking dish. Brush with olive oil; season with salt and pepper.
When finished baking, remove sweet potatoes from oven and increase temperature to 400°F. Bake chicken until it reaches 165°F, 25–30 minutes. Remove chicken from oven, tent with foil and rest for 5 minutes.
Turn oven to broil and line a baking sheet with foil. Arrange broccoli florets in a single layer and evenly coat with cooking spray; season with salt and pepper. Broil broccoli until lightly charred and crisp-tender, 8–10 minutes.
Cut chicken into bite–sized pieces and combine with broccoli florets, chickpeas, chives, and lemon zest in a large bowl.
Cut a slit length–wise down each sweet potato, making sure not to cut through the bottom or sides, creating a pocket. Gently press ends of sweet potatoes to open the “pocket”. Fluff the flesh of the sweet potatoes, removing some flesh to make room for the filling (reserve for a other use).
Spoon chicken filling into each sweet potato and drizzle with Avocado Green Goddess Dressing.