Vieques Recovery and Redevelopment Act This bill provides a framework to compensate certain residents of the island of Vieques, Puerto Rico, for the use of such island for military readiness. The bill sets forth provisions regarding award amounts for individuals and for claims by the municipality of Vieques. An individual claimant who has resided on the island of Vieques for not less than five years before this bill's enactment and files a claim for compensation with the Special Master shall be awarded monetary compensation if it is more likely than not that the claimant contracted a chronic, life threatening, or physical or mental disease or illness as a result of the U.S. government having used the island for military readiness. Total amounts awarded under this bill shall not exceed $1 billion dollars. A claim to which this bill applies shall be barred unless filed within 15 years of this bill's enactment. Notwithstanding any contract, a representative of an individual may not receive, for services rendered in connection with a claim of the individual, more than 20% of a payment made under this bill.