If using wooden skewers, soak in water for 30 minutes prior to use.
In a small saucepan, whisk together miso, sugar, sake, and mirin. Heat over medium heat until sugar dissolves and the sauce becomes smooth, whisking constantly. Remove from heat.
Preheat grill to high heat (or high on broiler if using oven).
Cut the chicken into 1 inch pieces. Remove the dark green part of the leeks, clean well, and cut into 1 1/2 inch pieces. Place the chicken and leeks alternately onto the skewers, starting and ending with chicken pieces.
Grill, turning about every 2-3 minutes and brushing with the miso glaze, until the chicken is cooked through.