Add chia seeds to a bowl. Whisk in the coconut milk. Cover and refrigerate overnight or for at least 6 hours.
If the chia pudding appears to be too thick the next day, loosen with a bit of water. (Heating it slightly helps remove any lumps.)
To make the compote, add fresh/frozen mango and sugar to a saucepan. Cover and cook until it starts to thicken, about 6-8 minutes. Break up the mango pieces with a spatula as it cooks.
To serve, layer the chia pudding and mango compote into glasses. For a simpler option, just spoon the compote over the chia and serve. Top with fresh mangoes.