Technically yes you can. Depending on which potatoes you use, if potatoes are quartered into smaller sizes they should cook through by the time the chicken is fully cooked. You should parboil the potatoes a bit if cooking the potatoes and chicken on the stovetop to ensure the potatoes are fully cooked. If you are baking in the oven, you should be ok to place everything in the oven without parboiling the potatoes.