Preheat grill to medium-high heat. Soak wooden skewers in water while you prepare the rest of the dish. It is not necessary to soak metal skewers.
Boil potatoes in water for about 7 to 8 minutes in salted water.
While the potatoes are simmering cut the chicken into large 1 1/2 inch pieces. Place chicken into the bowl and stir in pesto sauce. Remove potatoes from water and drain. Place potatoes in a small bowl and drizzle 1 tablespoon of olive oil over potatoes and stir to coat the potatoes with olive oil.
Assemble kabobs by placing a potato on the skewer and then alternate between chicken and potatoes until your skewer is full. Try to end the skewer with a potato, as it will keep the chicken in place. Place kabobs on the grill and cook for 10 to 15 minutes turning 1/4 turn every 2 or 3 minutes. On the last turn of the chicken squeeze the juice of 1 lemon over the kabobs. Cook chicken until it is fully cooked. Serve immediately. These kabobs go wonderful on top of a salad.