Despite major technological advances, management of type one diabetes mellitus (T1D) remains suboptimal, putting millions of people at risk for immediate and long-term complications. After meals, a mismatch between carbohydrate absorption rate and insulin action typically leads to alternating periods of hyper- and hypoglycemia. A conceptually promising approach to control both problems is dietary carbohydrate restriction to reduce postprandial blood glucose changes and insulin needs. In a prior survey study, the investigators documented exceptional glycemic control (HbA1c 5.67%) and low acute complication rates among 316 children and adults with T1D consuming a very-low-carbohydrate diet. To test the feasibility of this approach, the investigators will conduct a randomized-controlled feeding study involving 32 adults and adolescents with T1D. Participants will be randomized to receive a very low carbohydrate vs. standard carbohydrate diet. Participants will be in the study for 12 weeks and receive all their meals by meal delivery.They will share continuous glucose monitoring data with the study team and be in close communication to adjust insulin doses as needed. All participants will have a screening visit, an individual or group education session, and 3 study visits to evaluate diabetes control and metabolic health. Some of these visits will have a fasting blood draw. Two of the visits will also comprise additional metabolic studies to assess glucagon response and brain function during hypoglycemia by magnetic resonance imaging (MRI). Participants will have IV catheters placed and receive IV insulin to drop blood glucose levels to 50 mg/dl for up to 30 minutes. The primary outcome will be HbA1c change from baseline. Secondary outcomes include detailed measures of glycemic variability, metabolic health, and quality of life.