Native CHamoru Equity Act This bill establishes a CHamoru Registry program. It also allows eligible Native CHamoru 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 CHamoru Registry program under the Office of the Governor of Guam. The program must keep a database to serve as a genealogy bank to verify Native CHamoru ancestry requirements. Next, it treats businesses owned by economically disadvantaged Native CHamoru 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 CHamoru 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.