“Eileen” is a chilly, immersive character study about a young woman drowning in the drudgery and burdens of the trap her life has become.

Eileen, played by the wonderful Thomasin McKenzie, has a soul-crushing job at a young men’s prison. And at the end of each workday, she drives her battered, smokey, exhaust-leaking Plymouth Savoy home to her alcoholic ex-police chief dad (Shea Whigham, hatefully perfect), but not before stopping at the liquor store to replenish his supply.

For this, she gets nothing but abuse and insults.

“You should be nicer to me,” she complains, to no avail.

It’s the winter of ’64-65 from the looks of things, and in this corner of Massachusetts, even “the beach” is bleak at this time of year. It’s no wonder Eileen fantasizes about the sex lives of others, and masturbates with images of a young guard or even of a silent young murder suspect in her mind.

And then this blast of big city sophistication, a well-dressed and perfectly-turned out beauty blows into her world. The new psychologist at the prison is a woman, a cool vivacious blonde vamped-to-the-max by Oscar winner Anne Hathaway. In this repressed, depressing, sexist world, Dr. Rebecca St. John is a breath of fresh air, an intellectual oasis, an ally and a confidante. Maybe even, when the chips are down, she could be a co-conspirator.

The latest film from the director of the Florence Pugh star vehicle “Lady Macbeth” is a vivid recreation of a time and a place in pre-feminist history, when males at any level, from loutish barflies to leadership in any institution — prisons included — had license to sexualize, demean and diminish women of real accomplishment.

In the case of “Dr. ‘Miss’ Rebecca St. John,” as her warden introduces her, we see somebody who may have to endure such loutishness, but maintains lines she won’t let any man cross, and a streetwise New York savvy about where to land a punch, and when.

With a relaxed, louche accent, stepping out of her “Thelma & Louise” T-bird, Rebecca gives off the air of New York money. But the very fact that this is a job she had to take speaks volumes. Hathway lets us see that least some of this men are just for “fun” post-Jackie Kennedy style icon act is a pose. Rebecca’s from the Midwest. Maybe all of it just an act.

The New Zealand-born McKenzie (“Jojo Rabbit”) is at her fearless best in bringing this mousie 24 year-old to sad-faced life. She’s a little embarassed to be reduced to wearing her dead mother’s finest when Rebecca asks her to join her for a martini at the local watering hole, timid in the face of a bullying boss (Siobhan Fallon Hogan) and deeply-ashamed of the ex-police chief father who keeps drunkenly brandishing a revolver at neighbors and kids, anybody to cross his aggrieved field of vision.

Eileen is all interior life, fantasizing not just about sex and escape but about that firearm — shooting herself or this hateful dead weight Dad who may have had reason to crawl into the bottle (her mother’s wasting death) but whose every breath is ruining Eileen’s life by limiting it.

Could the alluring, seemingly-uninhibited Rebecca be the answer to her prayers?

That’s the promising milieu peopled with vivid, complicated characters that “Eileen” immerses us in. And then, just as we’ve started to savor all the possibilities presented by this set-up, director William Oldroyd and screenwriters Luke Goebel and Ottessa Moshfegh take an abrupt, lurid and predictably melodramatic turn, and “Eileen” goes right off the rails.

The viewer can embrace this, rationalize it, give the filmmakers the benefit of the doubt and soldier on, accepting what transpires as daring and “dark.” Or you stare this blunder down and note that the saving grace of giving Marin Ireland a chewy scene as the mother of a murder suspect/patient of Rebecca’s is hardly justification for running “Eileen” right off the road, into the ditch, flipped, its Plymouth Savoy tires spinning in the winter chill.

Rating: R (Violent Content|Sexual Content|Language)

Cast: Thomasin McKenzie, Anne Hathaway, Shea Whigham and Marin Ireland.

Credits: Directed by William Oldroyd, scripted by Luke Goebel and Ottessa Moshfegh. A Neon release.

Running time: 1:36