Preheat the oven to 350°F and grease or line an 8×8-inch baking pan or 9-inch round pan with parchment paper.
In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt.
In a separate large bowl, whisk the Greek yogurt, sugar, butter, eggs, and vanilla until smooth.
Add the dry ingredients to the wet ingredients and gently stir until just combined.
Fold in the chocolate chips, reserving a small handful for the top.
Pour the batter into the prepared pan and sprinkle the remaining chocolate chips over the top.
Bake for 22–26 minutes, until a toothpick inserted in the center comes out with moist crumbs.
Let the cake cool completely, then dust generously with powdered sugar before slicing and serving.