Preheat a barbecue grill or chargrill pan over medium-high heat. Brush chicken all over with oil. Cook chicken for 4 minutes on each side or until cooked through. Transfer to a plate, cover loosely with foil and rest for 2 minutes. Thickly slice.
Meanwhile, cook noodles according to packet instructions. Drain.
Heat satay base, peanut butter and ¾ cup water in a large frying pan over medium heat until mixture starts to simmer and thicken. Reserve ½ cup satay sauce. Add noodles to pan and toss to coat.
Divide noodles among bowls. Top with chicken and spoon over a little of the reserved sauce. Scatter over peanuts and coriander. Serve with lime wedges and remaining reserved sauce