Preheat oven to 200°C – this may seem hot, but the skin needs to be crisp and the flesh succulently tender.
Place snapper head into a large bowl, toss with olive oil and sea salt. Massage oil and salt into the back of the head. Line a shallow baking tray with baking paper. Place the head facing upwards, resting on its gill flaps. Bake for 40 minutes until the skin is crisp, the is eye opaque, and the flesh is translucent and can be easily pulled away from the bone. Remove from the oven and set aside for 15 minutes before serving.
To make the sauce, bring water, lemon juice and zest to the boil in a small saucepan. Gradually whisk in the butter to form a smooth emulsion. Stir in chopped chives and capers. Season.
To assemble, carefully transfer the head to a large serving dish. Spoon the lemon caper butter over the fish and serve.