Native Chamorro Equity Act This bill establishes a Chamorro Registry program. It also allows eligible Native Chamorro organizations to qualify for federal contracting opportunities through their participation in certain small business programs that are administered by the Small Business Administration. First, the bill establishes a Chamorro Registry program under the Guam Department of Chamorro Affairs. The program must keep a database to serve as a genealogy bank to verify Native Chamorro ancestry requirements. Next, it treats businesses owned by economically disadvantaged Native Chamorro organizations as socially and economically disadvantaged small businesses for purposes of the Minority Small Business and Capital Ownership Development program, which is commonly known as the 8(a) program. Further, it allows businesses that are owned by Native Chamorro organizations to participate in the Historically Underutilized Business Zone Empowerment Contracting (HUBZone) program. The 8(a) program and the HUBZone program each limit competition for certain government contracts to participating small businesses.