FOR PEANUT SAUCE: Stir all ingredients in small saucepan over medium heat until thickened, about 2 minutes. Season with salt and pepper. Transfer to small bowl. (Can be made 3 days ahead. Cover; chill. Microwave on low setting until lukewarm and stir well before serving.).
FOR CHICKEN: Grind first 7 ingredients in processor to coarse paste. Heat oil in medium skillet over medium heat. Add paste to skillet; do not clean processor. Sauté paste until just brown, about 5 minutes; transfer to large bowl and cool. Add chicken and salt to processor; grind coarsely. Mix chicken into paste in bowl.
Press 1/4 cup chicken mixture around thick portion of 1 lemongrass stalk in 4-inch-long sausage shape, leaving 1 inch of stalk exposed. Repeat with remaining chicken mixture and stalks. (Can be made 2 days ahead. Place on plastic-lined baking sheet, cover, and chill.).
Spray grill with nonstick spray and prepare barbecue (medium-high heat). Grill satays until chicken is cooked through, turning often, about 8 minutes. Serve with warm peanut sauce.