Born in Sacramento, California, he threw and batted right-handed and was listed as 6 feet 1 inch (1.85 m) tall and 190 pounds (86 kg).

Palmer graduated from Norte Del Rio High School and attended American River College, both in Sacramento.

He was selected by the Philadelphia Phillies in the first round (sixth overall) of the 1966 Major League Baseball draft (secondary phase).

Palmer was called up to the Phillies after posting a 36–17 won–lost record in 31⁄2 minor league seasons, with 534 strikeouts in 516 innings pitched.

He made his major league debut on June 21, 1969, with a starting assignment against the Pittsburgh Pirates at Connie Mack Stadium.