Position an oven rack in the center of the oven and preheat to 400 degrees F. Line a rimmed baking sheet with foil and set a wire rack inside the baking sheet.
Prick each of the sweet potatoes 5 times with a fork and place on the rack, keeping space in between to allow the heat to circulate. Bake the sweet potatoes until a paring knife can easily go through without resistance, about 45 minutes. Remove from the oven and allow to cool completely. Keep the oven heated to 400 degrees F.
Line a baking sheet with parchment. Dividing evenly, brush both sides of each pita half with the olive oil using a pastry brush, and season the inner side of the pitas with the smoked paprika and 1/4 teaspoon salt. Cut each seasoned pita into 6 wedges, then arrange in a single layer on the prepared baking sheet. Bake until lightly golden and crisp, 6 to 8 minutes. Allow to cool completely.
Once the sweet potatoes are cool, scoop the flesh (about 1 1/2 cups total) into a food processor and add the yogurt, brown sugar, lemon juice, garlic powder, cumin, 2 teaspoons salt and several grinds of black pepper. Process until combined, scraping down the side of the processor bowl to make sure yogurt is fully incorporated. Transfer the dip to a serving bowl and gently fold in the chives. Serve at room temperature along with spiced pita chips.