Creating Access to Residency Education Act of 2014 - Amends the Public Health Service Act to direct the Administrator of the Centers for Medicare & Medicaid Services (CMS) to make grants to or enter contracts with eligible entities to support the creation of new medical residency training programs or slots within existing programs in states in which there is a low ratio of medical residents relative to the general population.

Requires an eligible entity to be: (1) located in a state with fewer than 25 medical residents per 100,000 population, and (2) a public or nonprofit teaching hospital or an accredited graduate medical education (GME) training program. Allows such entity to enter into a partnership with a state, local government, community health center, local health department, hospital, or other appropriate organization.

Requires a grant or contract agreement: (1) in the case of a new or existing medical residency training program in the field of primary care, to require the recipient to provide one-third of the cost of the slots to be funded and to require the Administrator to provide the remaining two-thirds of such cost; and (2) in the case of such a training program in any other field, to require the recipient to provide one-half of the cost of the slots to be funded and the Administrator to provide the remaining half.

Directs the Administrator to establish application processes for eligible entities to receive funding, including multiyear commitments to ensure the continued funding of GME slots for residents in training.