Preheat oven to 300°F. Line 2 large rimmed baking sheets with parchment paper.
Place 1 cup chocolate chips in microwave-safe bowl; microwave on low setting at 30 second intervals, stirring occasionally, until chocolate is melted. Cool slightly.
Using electric mixer beat egg whites and salt in medium bowl until soft peaks form. Gradually add sugar, then vanilla, beating until whites are thick and glossy.
Fold in melted chocolate and coconut, then remaining 1/3 cup chocolate chips.
Drop batter by heaping teaspoonfuls onto prepared sheets, spacing 1 1/2 inches apart.
Bake cookies 10 minutes. Reverse sheets. Bake until tops are dry and cracked.