The chimp bonds with his human mother, but is jealous of her husband and ransacks his library, becoming increasingly unmanageable. Along the way, viewers watch Nim learn to dress himself, do household chores such as wash the dishes and endear himself to all the humans who work with him.
Because Nim's life was one big science project, Marsh was able to obtain vintage footage from the 1970s, which he uses with present-day interviews.
"I admired Stephanie [LaFarge] enormously," he said. "There was no text book on how to bring up a chimp. The breast-feeding was kind of weird, but her whole mission was to treat him just as a child."
The bell bottoms, VW buses and pot-smoking caretakers of Nim paint a colorful picture of that flower-power era. Nim himself partakes in the occasional cigarette, beer and even a puff of weed.
It was the era of psychologist-behaviorist B.F. Skinner, a mentor of professor Terrace's, and nurture was expected to triumph over nature. Now scientists know better.
The ensuing chaos at LaFarge's home prompts Terrace to remove Nim and place him with psychology student Laura-Ann Petitto, who becomes his second mother. She and other teachers move to Delafield Estate, a mansion in the Bronx owned by Columbia and bring the chimp back and forth to the lab to learn sign language.
He makes great progress, learning 125 signs and even creating his own favorite sign, "play."
His play gets rougher, however, and Nim bites Petitto, who requires 37 stitches. By the age of 4, Nim mauls another researcher in the face and Terrace abandons the project.
Nim is sent back to Oklahoma where he sees other chimps for the first time in his life and has no idea how to relate to them.
When the primate center runs out of money, Nim is shipped off to a small cage at a research lab at New York University supervised by Dr. James Mahoney.
But Mahoney soon begins to see the research as inhumane and secretly collaborates with one of Nim's favorite caretakers from Oklahoma, Bob Ingersoll, to free him.
Nim is moved again to Black Beauty Ranch, a Texas sanctuary mostly for abused horses. Isolated and lonely, Nim accidentally kills a poodle. When his first mother, LaFarge, returns to visit, Nim recognizes her, but goes into a rage, stopping just short of killing her.
Ingersoll, an evolutionary biologist who had befriended Nim while working at the Oklahoma Primate Center, visits the sanctuary, as well. Nim was angry at first, but is quick to forgive, signing "play" to his old playmate.
"I knew how to be a chimp," Ingersoll said. That involved long walks, "rolling around and tickling and slapping each other," climbing trees and "thinking like a 9-year-old kid," he added.
Ingersoll had no reservations about Nim's animal nature. "I had worked with chimps before," he said.
"But he had a real accessible personality," Ingersoll said. "He was not a tense, uptight, kind of nervous chimp. ... He was pretty easy, at least for me. I felt for him and, in a way, I could relate to him."
The film villainizes Terrace, whose project set the unique life of Nim in motion. But he told ABCNews.com that his work was in the early 1970s, before scientists had been sensitized to animal rights.
"Everyone I know was blind to this issue," he said.
The film treated the project "as is if it happened yesterday, not 35 years ago," he said, calling it "dishonest."
Terrace said he had indeed bonded with Nim and had pushed for the chimp's release from the research lab.
"They said I made no scientific discovery, that the whole project was a waste in terms of science," he told ABCNews.com.
In a 1979 article in the magazine Science, Terrace wrote that after initialing thinking he had partial evidence of grammatical ability in an ape, he discovered that Nim was actually "imitating" his teachers' sign language.
"A negative result can be as important as a positive one," he said.
As a researcher, Terrace said he still believes animals do not have the same emotions as humans.
"There is no evidence of that," he said. "Part of the human condition is that we are brilliant anthropomorphizers. We project our feelings on them."
But biologist Ingersoll disagrees. Now 58 and an animal rights activist, he said that he hopes the documentary will help raise awareness and funds for the plight of the 937 remaining NIH chimps.
He pushed for passage of the Great Ape Protection and Cost Savings Act, which passed a key Senate committee in July and would phase out invasive experiments on chimps.
Ingersoll has said the warehousing of chimpanzees for experimentation is "fundamentally inhumane."
"It's an aged population of veterans who have gone through their entire lives working for us and it seems they deserve to be retired," he said.
According to Ingersoll, however, chimp sanctuaries are expensive to operate and already at capacity. Yearly maintenance for a single chimp is $10,000 to $15,000.
"We would have to build a place in the hundreds of millions and then get them there, but it can be done," he said.
Ingersoll and Nim continued their play dates until the chimp died of a heart attack at 26. Chimps in captivity can live to 55 or 60.
Ingersoll said stress could have played a role in Nim's early death, but suspects something else: "It might actually be fair to say he died of a broken heart."