Place 20 wooden skewers in water to soak. In a large, shallow dish, combine the yogurt, lemon juice, garlic, sugar, turmeric, salt, and pepper.
Add the chicken to the yogurt mixture and toss to coat. Cover with plastic wrap and refrigerate at least 15 minutes (or overnight, if desired).
Heat grill to medium high. Remove the chicken from the marinade, shaking off the excess, and thread onto the skewers.
Grill the chicken, turning, until cooked through, 3 to 5 minutes. Transfer to a platter and cover with foil to keep warm.
Grill the mango until slightly charred and tender, about 2 minutes per side. Serve with the chicken.