Chronic Disease Management Act of 2021 This bill modifies requirements for health savings accounts (HSAs) to permit the high deductible health plans required for an HSA to provide care for chronic conditions with no deductible. The bill covers any preventive care service or item used to treat a chronic condition if (1) such service or item is low-cost, (2) there is medical evidence of the effectiveness of such service or item, and (3) there is a strong likelihood that the use of such service or item will prevent the exacerbation of the chronic condition or the development of a secondary condition that requires significantly higher cost treatment. The bill further provides that an individual who has been prescribed preventive care for any chronic condition may be presumed to have been diagnosed with such condition if such preventive care is customarily prescribed for such condition.