Whisk yogurt and next 9 ingredients in large bowl to blend. Add chicken and turn to coat. Cover and refrigerate overnight.
Combine all ingredients in medium bowl. Season to taste with salt and pepper. (Chutney can be made 1 day ahead. Cover and refrigerate.)
Prepare barbecue (medium-high heat). Brush grill with oil. Transfer marinade-coated chicken to barbecue grill. Grill chicken until cooked through, about 7 minutes per side. Transfer chicken to cutting board. Cut crosswise on diagonal into 1/2-inch-thick slices. Transfer to platter. Serve with chutney.