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Preheat oven to 350ºF. Grease a 9-inch round baking pan, and line the bottom with a cut-out round of parchment paper.
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In a medium bowl whisk together the flour, cocoa powder, baking powder, and salt. Set aside.
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In a large bowl, mix the sugar, yogurt, eggs, vanilla, and olive oil together until combined.
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In batches, mix the flour mixture into the yogurt mixture and gently stir until combined. Fold in the chocolate chips, and then pour the cake batter into the prepared pan.
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Bake for 40 to 45 minutes or until a toothpick inserted into the center comes out clean.
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Cool the cake in the pan for 15 minutes in a rack; then gently run a knife along the side of the cake. Carefully invert the cake onto a plate and then invert again onto a cooling rack to cool completely.
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Serve alone, dusted with powdered sugar, or add a scoop of vanilla ice cream.