 This pilot study will be conducted in adolescents with cystic fibrosis CF without diabetes but with abnormal glucose tolerance, and will assess the effects of sitagliptin on glucose regulation. An oral glucose tolerance test OGTT and a mixed meal tolerance test MMTT, will be performed at baseline and again 4 weeks after treatment with study drug. We will also look at blood sugars throughout the day using a continuous glucose monitor CGM before each time the MMTTOGTT are performed. Several hormones that may affect the way the body regulates blood sugars will be measured in blood when the OGTT and MMTT are done. We will assess the effect this medicine has on blood sugars using CGM and the effect the medicine has on the hormones measured during the OGTT and MMTT. 