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Preheat the oven to 350°. Line a large rimmed baking sheet with parchment paper. In a medium bowl, mix the coconut with the turbinado sugar, egg whites, vanilla and salt. Transfer the macaroon mixture to the prepared baking sheet and pat it into a 12-by-4-inch rectangle 1/2 inch thick. Bake for 25 minutes, or until golden around the edge. Let cool.
Meanwhile, in a medium saucepan, combine the granulated sugar and water and cook over moderately high heat until reduced by a quarter. Add the chestnuts and rum and cook over moderate heat, stirring occasionally, until the chestnuts are coated in a thick syrup, about 15 minutes. Pour into a bowl and let cool.
In a medium glass bowl, combine the chocolate and cream and melt in a microwave oven on high for 1 minute, stirring halfway through.
Transfer the macaroon rectangle to a platter and arrange the chestnuts on top in 3 rows of 12. Pour the chocolate over the entire top of the macaroon rectangle. Let stand at room temperature for 30 minutes, or until set. Slice into bars and serve.
The chocolate-covered macaroon rectangle can be refrigerated for up 2 days. Bring to room temperature before slicing.