Palmer was drafted by the Montreal Expos in the 21st round (489th overall) of the 1976 amateur entry draft. He pitched in the Expos organization until 1985. Although he made his major league debut in 1978, he pitched only a handful of minor league games in 1981 due to injuries, and had to fight his way back from Triple-A in 1982, where he made nine minor league starts. Additionally, he did not throw a single pitch in 1983 due to further injuries.
