If you knew the day you were going to die, how would you choose to live? This is the question at the heart – and on the cover – of American author Chloe Benjamin’s second novel, The Immortalists (her first, The Anatomy of Dreams, was not published in the UK). Given the catchy Hollywood-style pitch, it is little surprise that the book has been snapped up by publishers across the globe and a TV adaptation is already in the works. Less predictable is just how engaging this bittersweet novel turns out to be.

Benjamin’s story starts in a sweltering New York apartment during the summer of 1969. The four Gold siblings are restless. Something, it seems, “is happening to everyone but them”. The oldest, Varya, is 13, the youngest, Simon, only seven, but it is 11-year-old Daniel who hears about the woman on Hester Street who can predict the exact date you will die, and nine-year-old Klara who summons up the courage to knock on her door. The experience unnerves them all. None of them wants to talk about it. Not until nine years later, shaken by the unexpected death of their father, do they finally share their dates with one another.

The novel unfolds over four parts, one for each of the siblings in order of their predicted deaths. Simon, who will die shortly after his 20th birthday, is determined not to risk wasting a moment: “What if the woman on Hester Street is right and the next few years are his last? The mere thought turns his life a different colour; it makes everything feel urgent, glittering, precious.” Abandoning their widowed mother, he and Klara escape New York for San Francisco, where Simon comes out and throws himself into the sexual free-for-all of the pre-Aids gay scene. Mercurial Klara, who will die in her 30s, pursues her lifelong fascination with magic, developing an act that will take her to Las Vegas. The two elder siblings stay in New York to take care of their mother. Daniel becomes a military doctor, Varya a scientist whose academic research with primates investigates the prolonging of life.

In an interview Benjamin has described her novel as “a book that explores how to live with uncertainty … It is an unbelievable, absurd paradox that we have to put one step in front of the other every day without knowing which one will be our last.” Taking each of her four characters in turn, she asks, is the knowledge a curse or a blessing? Does it liberate you to live life to the full or does it hobble you, stripping you of agency? What is it that you choose to believe in? By leaving open the question of whether the clairvoyant is a seer or a fraud, Benjamin allows each of the siblings to react in their own way, in accordance with their nature. It is the clairvoyant herself who quotes Heraclitus’s epigram: character is fate. “You wanna know the future?” she asks Varya. “Look in the mirror.”

Benjamin is trying to do a lot in this novel and it doesn’t always work. Sometimes she shows her workings too clearly: musing on her siblings, Varya wonders how they could “diverge so dramatically in their temperaments, their fatal flaws”. The investigation Varya is conducting into human longevity is too heavy-handedly metaphorical for its own good. Benjamin has researched her material meticulously and too much information makes its way undigested on to the page; there are also several moments where the plot veers towards the preposterous.

But despite these cavils The Immortalists worms its way under your skin. Benjamin writes with verve and charm and her four protagonists are resolutely real. She is particularly good at the sibling bond, the unbreakable ties that bind brothers and sisters together even as they drive each other to distraction. The novel begins in Technicolor, with all the eager vitality of youth, and gradually slows and darkens as the weight of loss accumulates, casting a long shadow over the siblings who remain. It is a testament to Benjamin’s skill that, as her story pulls focus from the wild nightclubs of the Castro and the glitter of Las Vegas to life in the suburbs, as youthful exhilaration and recklessness give way to grief and anger and frustration and fear, the novel itself does not narrow but instead grows deeper and more absorbing. As for the question posed on the book’s cover, Benjamin offers no easy answers. I am willing to predict that The Immortalists will see book groups across the UK vigorously debating the issue.

• Clare Clark’s latest novel is We That Are Left (Vintage). The Immortalists by Chloe Benjamin (Headline, £16.99). To order a copy for £14.44, go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min. p&p of £1.99.