The Golden This, That, and the Other Thing Family
Christine Ammer, The Facts on File Dictionary of Clichés, second edition (2006), has this entry for golden parachute:
golden parachute An employment agreement that gives generous benefits to its high-ranking executives if they are dismissed owing to a company merger or takeover. This term, dating from about 1980, may have been based on the older golden handshake, which offers an employee generous benefits in exchange for early retirement. It dates from the mid-1900s, when a dwindling school population prompted many localities to offer such an incentive to teachers. In contrast, golden handcuffs are a financial incentive to keep an employee from leaving a company. Stock options that can be exercised only far in the future are a popular form of golden handcuffs. This term dates from about 1970.
The earliest mention of "golden handshake" in Google Books search is an item from The Times Intelligence Department, Cuttings From The Times:
On the Stock Exchange Ordinary share values were up by £3,000m. since 1955 — not a bad figure, and pretty healthy for those who happened to hold enough. They all knew what happened when the takeover bid got going: a a 50 or 60 per cent rise in values, and the golden handshake for people pushed out.
Although Ammer doesn't say so, the term "golden handshake" appears to have originated in the UK, to judge from the early Google Books matches. Many are from the early and middle 1960s.
As for "golden handcuffs," a BusinessWeek article from 1974 uses both that term and "golden carrot" (though not "golden stick," apparently):
Golden handcuffs. Instead of using the golden carrot, some companies try to put "golden handcuffs" on their key people, paying them well but holding back a substantial part of compensation, which is forfeited if the man resigns.
But The Western Socialist (1969) takes a more class-conscious approach to the term "golden handcuffs" and sees them as serving a specifically anti-proletarian purpose:
THE "GOLDEN HANDCUFFS"
Bourgeois economists include fringe benefits as an addition to wages. Class conscious workers label such "additions," particularly pension plans, as the "workers' golden handcuffs." The grand design of pension plans and other "fringe" benefits is to create a feeling almost of partnership among the workers and thus give them added incentive to be satisfied with their inadequate lot.
The plague of erroneous dates
Unfortunately, Google Books is quite unreliable as a tool for finding recent first occurrences of business and government related terms. In the first place, almost all of its results are in snippet form with no access to the front of the book to check its publication date. One of the Google Books search results that Josh61 cites in a comment above, for example,comes from Congressional Quarterly Weekly Report with a nominal date of 1956; however, it includes a quotation from Kenneth A. Cook, identified as president of the Environmental Working Group, even though the EWP website reports that the group has existed for only 20 years.
Likewise a link to Page's Ohio Revised Code Annotated carries the year 1953, but the snippet views show citations to publications from 1990 using the term "golden parachutes." Statute books and government collections are notorious for posting the initial date of content in the collection without acknowledging that subsequent revisions may be included from years or even decades later.
The Wikipedia article that Erik Kowal cites in a comment above may well be right that the first instance of "golden parachute" to describe executive-protection provisions in employee contracts goes back to 1961, but I couldn't find any contemporaneous confirmation in print that the 1961 Trans World Airlines financial arrangement was called a "golden parachute" provision at the time. if it was, it must have been something of an outlier, because date-confirmable matches for "golden parachute" are hard to come by until about 1983. In 1984 and 1985, the usage seems to explode.
One instance of "gold parachute"—from Private Eye magazine (probably in 1983) [combined snippets]—extends the parachute metaphor:
Former shareholders in Letraset may be justifiably bemused at exactly how their former chairman in managed to come away with a record "solid gold parachute" worth approaching £700,000 when he jumped out following the 1981 takeover by the Swedish group Esselte. After all, his salary the year before had only been £53,000 and and though he was on a remarkable four years' notice that still leaves a big unexplained gap. The answer may well lie in suggestions that salary was only one of the "perks" justifiably enjoyed by the persuasive Fieldhouse for presiding over the declining Letraset.
Why 'golden parachute'?
People sometimes wonder about the aptness of the term "golden parachute." After all, gold is an unusually heavy metal (heavier than lead by volume), so it doesn't make an intuitively good choice for parachute material, valuable though it is. A passage in Anthony Bailey, The Mother Tongue (1961) [combined snippets] may shed some light on how the term might have come to be considered suitable:
For the occasion Laver had dug out an RAF blazer, on the lapel of which was clipped a small gold parachute—indicating that he had successfully bailed out from a plane during the war. He was wearing a reasonably clean white shirt and a tie that, although bought on Madison Avenue, quite closely resembled the regimental stripes of the Coldstream Guards.
The U.S. Navy evidently had a similar award, referred to as "gold parachute wings." From Naval Aviation News, volume 55 (1973):
Gold Wings for Jumper
Christchurch, N.Z. — WO William S. Couch has received his gold parachute wings as a member of the Navy's only pararescue team. The wings represent Couch's tenth parachute jump from an aircraft and were earned in just two and a half months.
Similar insignia are reported for the U.S. Marine Corps (a "gold parachute insignia," in 1967) and the U.S. Army (an insignia of a "gold knight's helmet superimposed on a gold parachute," in 1969).
So the the idea that leaving employment with the security of a big money payoff is comparable to bailing out of a plane with a solid-gold parachute to soften one's landing may have been suggested by the RAF's practice during World War II of awarding wartime parachutists "small gold parachute" lapel pins for successfully bailing out as needed.