President Carter, first chief executive from the Deep South since the Civil War, is losing that region's suport, a new poll of registered voters shows.

The poll was conducted in Virginia and nine other southern states by Darden Research Corp. of Atlanta. Major findings include:

Southern Democrats now favor Massachusetts Sen. Edward M. Kennedy over Carter.

Southerners who say they voted for Carter in 1976 now favor Kennedy over The Georgian.

Among Southern Democrats, Republicans and independents, former California govenor Ronald Reagan, a Republican, is now favored over Carter.

"Regan is the frontrunner not only in the country but the South - the bastion of Carter support," said Claibourne H. Darden Jr., president of the nationally knowsn public opinion research firm.

The Darden poll interviewed 750 registered voters by telephone between June 26 and 29 in 87 localities of the South. The research firm sponsored the survey.

One question: "If Ted Kennedy was running against Jimmy Carter for persident, who would you favor?"

Among respondents overall, the result was almost a tie - Carter 42.9 percent - responded that they would never consider voting for Brown. Kennedy was second highest in this negative rating with 28.8 percent. Connally was third at 27.3, and Sen. Bob Dole (R-Kan.) was fourth at 25.6 percent. CAPTION: Picture 1, EDWARD M. KENNEDY . . . leads among Democrats; Picture 2, RONALD REAGAN . . . southern front-runner