Melt coconut oil in a small saucepan over medium heat. Add peaches and cook for about 2-3 minutes. Then add vanilla, maple syrup, and cinnamon and cook for another minute. Remove from heat.
In two containers with lids, divide the oats, milk, chia seeds, and peach mixture and stir to combine. Cover and refrigerate overnight (about 8 hours). Serve hot or cold. Overnight oats are best eaten within two days.