The planning of Rickover Naval Academy began in the spring of 2003. Current Academy Superintendent Michael Biela was selected to spearhead the planning of what was then called the Chicago Naval Military Academy. As the school came closer to opening (Spring 2005), Mr. Biela enlisted the help of CDR Donna Fournier, Mr. Scott Fogel, CPT James Patterson, and Mr. Derrick Svelnys, who later became teachers at Rickover, to complete the task of planning the academy. Decisions had to be made on everything from the school policies to the four-year curriculum to the paint colors of the classrooms. The name was changed to Hyman G. Rickover Naval Academy after Mrs. Eleanore Rickover gave permission to name the school after her late husband, Admiral Hyman G. Rickover, a 1917 Chicago Public Schools graduate and 1921 United States Naval Academy graduate.
RNA was to be located on the north side of the city, which was not being served by a JROTC academy. After evaluating several potential locations, Senn High School was chosen due to the availability of space in the building. Via the staunch support of Mayor Richard M. Daley, 48th Ward Alderman Mary Ann Smith, and the Chicago Public Schools, the plans for RNA moved forward. A $2.1 million dollar grant was awarded by the U.S. Navy to start the academy. Most of the grant covered capital improvements to the RNA spaces, the campus lunchroom, the campus library, and a Senn science lab.
For the 2019-2020 school year Rickover will be moving to its own building at 5700 W. Berteau Ave., the former home of the now-closed Luther North High School in Chicago's Portage Park neighborhood.
On September 6, 2005, Rickover Naval Academy opened its doors with approximately 120 cadets and 12 staff members. RNA has continued to grow to over 450 cadets and a staff of over 35. The first graduating class was awarded $3.1 million in scholarship monies. Rickover has risen to become a top-20 high school by Chicago magazine and in the top 25 in Illinois by US News and World Report.