Whisk the sugar, egg whites, vanilla, and salt in a large bowl until frothy. Whisk in the butter, flour, and cinnamon until blended. Stir in the chocolate chips.
Brush the pizzelle cooking surfaces with melted butter. Spoon 1 tablespoon of batter in the center of the pizzelle iron. Close the iron and cook until deep golden, about 3 minutes. Transfer the pizzelles to a cooling rack. Cool completely. Store the pizzelles airtight at room temperature.
Chef's Note: The batter can also be cooked in a preheated and lightly oiled waffle iron. Pour 1/2 cupfuls of batter into the waffle iron and cook for about 3 minutes.