Chabert served in the Louisiana House of Representatives from 1972 to 1980, along with Dick Guidry, Morris Lottinger, Jr., and Elward Thomas Brady, Jr., who represented other districts which included a portion of Terrebonne Parish. and in the Louisiana State Senate from District 20 from 1980 until 1992. In 1983, Chabert won his second term in the Senate in a general election race against fellow Democrat, Glenn F. Voisin, 19,530 votes to 15,862. In 1987, Chabert was again forced into a second race with Glynn Voisin. The third-place candidate, Elward Brady, had switched to the Republican Party and finished with 19.6 percent of the vote in the nonpartisan blanket primary. In the general election, he defeated Voisin once again but narrowly, 17,419 to 16,405. Chabert died near the end of his third Senate term and was succeeded for one term by son, Marty James Chabert, an easy winner over the Republican Paul E. Brown. A younger son, Norby Chabert of Houma, was elected to the same seat in a special election held in August 2009, upon the resignation of Reggie Paul Dupre, Jr., who had succeeded Marty Chabert in 1996. Like his father and brother, Norby Chabert held Democratic Party allegiance. In 2011, however, Norby Chabert switched to the Republican Party, which had already become the majority in the chamber.
Leonard Chabert was employed at some point after 1988 and prior to his death at the Pennington Biomedical Research Center in Baton Rouge. The Leonard J. Chabert Medical Center in Houma, a regional acute-care facility, is named in his honor. The center began in 1978 as a teaching hospital providing clinical training to medical students and physicians. In 2009, LJCMC completed a study of patients suffering from heart failure. Some 42 percent of the patients there are Medicaid recipients. LJCMC is a surgical facility too; it has 156 beds. In his Senate campaign, Norby Chabert recalled his father's dedication to bringing Chabert Medical Center to Acadiana:
Not only did my father bring the Impossible Dream of a charity hospital to the bayou region, but he fought every session, not only to have it funded, but he fought to keep its very doors open. He knew what it was like to grow up poor and have no health care.... It was his life's mission to take care of the sick and the uninsured of the bayou region. Upon his death, his legacy of fighting for the medical center was rewarded by having "his hospital" renamed in his honor.... Chabert Medical faces the same deep cuts that used to keep my father awake at night wondering how he would overcome the funding shortfalls that threatened its closure....
