With the rack in the middle position, preheat the oven to 350°F (180°C). Line a baking sheet with parchment paper or a silicone mat.
In a bowl, combine the oats, coconut and oil.
In another bowl, whisk the egg white until frothy. Gradually add the sugar, whisking constantly, until soft peaks form. Add the meringue to the oat mixture and stir until just moistened. Scatter the mixture onto the lined baking sheet and press together to form small, loose clusters.
Bake for 20 minutes, stirring gently several times during cooking. Let cool on the baking sheet. The coconut oat crunch will keep for up to 3 weeks in an airtight container at room temperature.