Combine chicken stock and quinoa in a saucepan and bring to a boil. Reduce heat to medium-low, cover, and simmer until quinoa is tender, about 15 minutes. Remove from heat.
Heat olive oil in a large skillet over medium heat until shimmering. Add asparagus, bell peppers, and onion; cook and stir until softened, about 6 minutes. Stir in chickpeas. Pour in 2 tablespoons balsamic vinegar and cook until reduced, about 4 minutes. Add lemon juice, salt, and black pepper. Stir in cooked quinoa. Drizzle 1 tablespoon balsamic vinegar over pilaf before serving.