Palmer was born in Nelson on 21 April 1942. At Victoria University of Wellington, he studied both political science and law, and was granted permission to practice law in 1965. After working for a time in Wellington, he attended the University of Chicago's law school, gaining a doctorate of law in 1967. He taught for a time at the University of Iowa and the University of Virginia, and undertook consultancy work for the Australian government. Eventually, in 1974, he was appointed to a professorship of law at Victoria University of Wellington, bringing him back to New Zealand again.
In 1979, Palmer was elected to parliament, having stood as the Labour Party candidate for Christchurch Central electorate. He eventually became deputy Leader of the Opposition in 1983. When, in 1984, the Labour Party won the general elections, Palmer became Deputy Prime Minister. He also became Attorney-General and Minister of Justice. After the 1990 elections, when Labour was reelected, he also became Minister of the Environment, an area in which he took personal interest.
The most notable feature of New Zealand politics at the time was the economic reform promoted by the Finance Minister, Roger Douglas. Douglas was advancing free market monetarist policies involving extensive privatization of state assets and the removal of tariffs and subsidies. These policies, which contravened Labour's basic policy platform and campaign promises, were deeply unpopular with the public, and resulted in a confrontation between Prime Minister David Lange and Roger Douglas. Eventually, Douglas was removed from Cabinet, but the dispute had weakened Lange enough that he resigned a month later. Palmer, being deputy leader, took over as Prime Minister.
Palmer, however, was perceived by the public as being too closely involved in Douglas's reforms. Of particular concern to many people was his work on the legal aspects of state sector rearrangement, such as his preparation of the State Owned Enterprises Act. The presence of David Caygill (a Douglas ally) as Minister of Finance further compounded perception that Palmer was doing nothing to address public concerns. The only area in which Palmer won praise from traditional left-wing supporters was in his handling of the Environment portfolio, which he kept when he became Prime Minister - it was his work here that eventually led to the creation of the Resource Management Act.
Two months before the 1990 elections, it was clear that Labour would not win. The damage done by Roger Douglas's reforms, as well as Palmer's perceived failure to address the issue, has caused too many Labour supporters to abandon the party. In addition, Palmer was perceived as being too academic and aloof, reminding people of the paternalistic "we know best" attitude that Douglas was accused of. Palmer was replaced by Mike Moore, who Labour believed would give it a better chance of winning. The attempt failed, however, and Labour was replaced by the National Party under Jim Bolger.
Palmer, who retired at that same election, later went on to serve as Professor of Law at Victoria University again. He also held a position as Professor of Law at the University of Iowa, and worked for a time as a law consultant. In 1994, he established Chen Palmer & Partners, a law firm he began with Wellington lawyer Mai Chen.