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.
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.
Pour 1 cup mole sauce over chicken in a medium bowl and toss to coat.
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.