Put the chocolate chips into a medium glass mixing bowl. Set aside.
Combine the milk, cocoa powder, sugar, vanilla and 1/4 teaspoon salt in a medium saucepan over medium heat. Whisk constantly until the cocoa is dissolved and the mixture comes to a simmer, 5 to 7 minutes. Remove from the heat and pour the milk mixture over the chocolate. Let stand for 5 minutes, then whisk gently until all the chocolate is melted. Whisk in the yogurt until smooth and blended, then cool completely.
Divide the mixture evenly among eight popsicle molds (about 1/3 cup per pop) and freeze until solid, at least 5 hours. (They'll keep up to a month.) Just before serving, briefly run the molds under hot water to release the pops.
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Be sure to cool the mixture completely before filling your molds; it will help with unmolding later.