In a large bowl, whisk 1/2 cup of the olive oil with the paprika. Add the chicken and toss to coat; let stand at room temperature for 15 minutes.
Meanwhile, in a small bowl, mix the yogurt, lemon juice, cayenne, crushed red pepper and the remaining 1 tablespoon of olive oil. Season with salt and black pepper and mix well.
Light a grill. Season the chicken with salt and black pepper and thread 3 pieces onto each of 8 skewers. Oil the grate and grill the chicken over moderate heat, turning occasionally, until golden brown and cooked through, about 10 minutes. Transfer the skewers to a serving platter and serve with the yogurt sauce and lemon wedges.
Make Ahead: The yogurt sauce can be refrigerated overnight.
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Recipe Credit: Jimmy Bannos Jr.
Image Credit: John Kernick