1. Heat a grill to high (450° to 550°). Meanwhile, heat oil in a medium saucepan over medium heat. Add onion and garlic and cook until softened, about 3 minutes. Stir in spices, sesame seeds, and almonds and cook, stirring, until fragrant, about 1 minute. Stir in tomato purée, broth, and chocolate chips.
2. Reduce heat to low and simmer, stirring often, until flavors develop and sauce thickens and darkens slightly, about 10 minutes. Purée in a blender with 1/2 cup water until smooth, about 30 seconds.
3. Pour 1 cup mole sauce over chicken in a medium bowl and toss to coat.
4. Grill chicken, turning once, until browned, about 8 minutes. Set chicken on a serving plate and sprinkle with minced chile and cilantro leaves. Serve with remaining mole sauce and lime wedges.
*Fruity, mild New Mexico chile powder is available at well-stocked grocery stores and Latino markets, but if you can't find it, you can leave it out and still have a flavorful dish.