Bring the water and the sea salt to a boil over high heat in a medium saucepan. Continually whisk with one hand, and at the same time slowly shake in the cornmeal in a thin stream with the other.
Lower the heat to medium and cook, stirring frequently, until the polenta thickens, about 20 minutes, depending on the coarseness of the grind. Scrape the bottom and sides of the pan while cooking to keep the polenta from sticking.
Stir in the olive oil, then pour into a bowl. Let it rest for 5 minutes before serving.