CHIMPANZEES share 96% of their genome with humans. If you were to credit the conceit of this charming novel, it would appear that we also share a love of gossip, wit, cinema, Brandy Alexanders and the quirky inversions and evasions that typify postmodernist fiction. Cheeta, aged 76 and the Guinness World Records title holder for the oldest chimp ever recorded, has outlived both Johnny Weissmuller, the greatest Tarzan, and Maureen O'Sullivan, better known as Jane, and, as these memoirs show, his bête noire – though he would pick me up on the use of the French phrase meaning "black beast" as a term of insult.

Me Cheeta is the literary equivalent of Cheeta's own "triple-back-flip-handclap-double-lip-flip-and-grin". In part, it is a wry and acid parody of the whole celebrity memoir genre. Cheeta's prose combines the mawkish generosity and barely concealed schadenfreude of many a veteran star. In the opening chapter, recounting an anecdote where Rex Harrison (with whom he worked on "Fox's disastrous megaflop Doctor Dolittle") stuck him up a monkey-puzzle tree, Cheeta describes him as "the universally despised, impotent, alcoholic, cruel, vain, brittle, snobbish and mephitic, but still, under the carapace of protective acerbity, very gentle and insecure human being". There's a long-running feud with Mickey Rooney, asides about the lecherous Chaplin, and a cocaine orgy with Constance Bennett. Cheeta, who has had the obligatory "battle with substance abuse", can still recollect in glorious Technicolor all the debaucheries and excesses of 1930s and 1940s Hollywood. The reviews that misspelled his name "Cheta" – glowing though they were – still rankle.

The novel is also about movies. Cheeta briefly escapes on his arrival in the Big Apple, and finds himself in a cinema – seeing, of course, all but the end of King Kong – and the writing shows that "Cheeta" can be poetic as well as wry. "It was exactly like a dream, I thought, all chopped up and shuffled, and then it hit me that it was, a dream, dreamed on to the wall by the silver-haloed heads in front of me." Cheeta proves himself quite the film theorist, reinterpreting the Tarzan movies as being about the ulterior tension between the primal, childish Tarzan and the tyrannical adult Jane, who constantly tries to bring "civilisation" to the jungle. Cheeta is reduced to the role of staff, rather than side-kick. As the series progresses, the real story becomes Cheeta's attempts to disrupt Jane's agenda. This culminates in Tarzan's New York Adventure. As he writes: "Chaplin had Hitler in The Great Dictator; I had Jane. I'll leave you and the American Film Institute to judge which was the more successful in skewering its target, only commenting that Maureen left Metro immediately afterwards, whereas I don't really think Hitler was very bothered by Chaplin's barbs, do you? Eh, Charles?"

Finally, it's about animals. Cheeta gleefully inverts many of the pious platitudes about humanity's relationship to animals. He is concerned about "endangered" animals, and observes that what endangers them is usually other animals in the jungle. "You know there are slightly more tigers in America today than there are left in the wild? It should be stressed that's not a cause for celebration just yet: the job's only half-finished." Zoos are "rehab"; where you get to eat bananas for the first time.

He adores humanity for its global warming, cigarettes and contraception, "omnicidal" though it is, and occasionally sticks up for the chimps, commiserating Gagarin on his anticlimactic role in the Space Race, pipped at the post by Ham.

All of this is delivered in glorious, inventive prose. A mamba "decanted" itself out its cage; he describes the "tweezers" of inverted commas around "civilisation". In a dream sequence in which he wins an Oscar, DiCaprio resembles a capybara, and Cheeta riffs "There's Mitch; there's Hitch; there's Clooney and Rooney; there's Marlene and Maureen and Mel. The Lumieres, the Fred Astaires, the Mayers and the players, and dearest Dolores Del". Moreover, there is a sneaky index with extra jokes (just check out how many men are billed "sexual relationship with Lupe Vélez"), a missing chapter and incredibly funny picture captions.

So who is "Cheeta"? The inventive paradoxes, supple prose and brilliantly geeky trivia resemble authors such as Jonathan Lethem, John Colapinto and Percival Everett. Jerry Stahl's last novel was the wonderful ventriloquism I, Fatty, which purported to be Arbuckle's memoirs. Quite honestly, I don't know – but whoever you are, I salute you.