Increasing Rural Health Access During the COVID-19 Public Health Emergency Act of 2020 This bill establishes, as part of certain grants for telehealth networks and resource centers, a pilot project to increase the use of remote patient monitoring technology in rural areas during the COVID-19 (i.e., coronavirus disease 2019) emergency. Specifically, the Health Resources and Services Administration (HRSA) must award grants to eligible entities in rural areas to coordinate care for individuals with chronic conditions and conduct other activities using remote patient monitoring technology. Eligible entities must meet requirements for participating in telehealth networks and must use appropriate technologies. Grant funds may be used, for example, to develop or acquire computer hardware and other equipment. In awarding these grants, HRSA shall give priority to entities that are capable of establishing programs quickly and that use technologies that provide continuous, real-time coaching services.