Medigap Protection Act of 1997 - Amends title XVIII (Medicare) of the Social Security Act to require the issuer of a Medicare supplemental (Medigap) policy to provide for certain enrollment periods during which an individual who is enrolled in a Medicare select policy, and who would be eligible to enroll under the issuer's Medigap policy at the time the individual became (or becomes) 65 years of age, may elect without prejudice coverage under any of the issuer's Medigap policies as a replacement for the Medicare select policy.