Preheat the oven to 200 degrees F. Line a baking sheet with parchment paper. Beat the egg whites and cream of tartar in a large bowl with a mixer on medium speed until frothy. Beat in the sugar; increase the mixer speed to high and beat until stiff peaks form, 5 to 6 minutes.
Transfer to a pastry bag fitted with a large round tip. Pipe 8 to 10 swirls on the prepared baking sheet. Bake until dry, 1 hour to 1 hour, 15 minutes. Transfer the baking sheet to a rack and let cool completely.
Put the chocolate chips in a microwave-safe bowl; microwave on 50 percent power until melted, about 1 minute, stirring halfway. Transfer the melted chocolate to a zip-top bag and snip a corner. Pipe the chocolate on the meringues to look like eyes.