Celebrating T'Pol's first full year with the Enterprise crew over dinner, Archer asks why her record states that she once took a five-day leave to visit an old Pennsylvania mining town called Carbon Creek. She claims Carbon Creek was the site of actual first contact between humans and Vulcans, long before the historical First Contact in 2063, and her second foremother (great-grandmother) was there. Trip Tucker scoffs at this, but then T'Pol offers to tell "the story."
T'Pol's ancestor, T'Mir, was on a survey ship with three other Vulcans investigating the launch of Sputnik, Earth's first artificial satellite, in October of 1957, when their impulse manifold malfunctioned and forced them into an emergency landing in a North American forest. The captain is killed, leaving T'Mir in charge of the surviving crew, Mestral and Stron. Not knowing whether their distress call to the High Command was transmitted in time, they use up their food rations within a week, then face the question of how they will survive. Despite the risk of cultural contamination, Mestral insists on visiting the nearby "settlement." Stealing clothes and hiding their ears to blend in with the locals, T'Mir and Mestral walk into Carbon Creek and enter a local tavern called the Pine Tree Bar & Grill. Realizing that "currency" is required, Mestral gets himself involved in a pool game for a bet. Quickly mastering the game's simple geometry, Mestral wins enough money for him and T'Mir to buy several bags of groceries. Trip interrupts T'Pol's story, skeptically comparing it to an old episode of The Twilight Zone, but he and Archer are intrigued, so she continues.
Hoping that a rescue vessel will eventually arrive, the three Vulcans take up residence in Carbon Creek and secure jobs — Stron as a plumber/handyman, Mestral as a coalminer, and T'Mir as hired help at the tavern. Despite their aim to stay to themselves as much as possible, Mestral becomes increasingly captivated by human culture, such as television and baseball, and by the townspeople themselves, particularly Maggie, the single mom who tends bar at the Pine Tree. After observing news reports of atomic bomb tests, T'Mir becomes convinced Earth is on the brink of self-annihilation, making their efforts to construct a subspace transceiver more urgent. But Mestral disputes that pessimistic view, seeing this species as empathetic and compassionate, and having great potential. In fact, Mestral makes excuses to leave the apartment so he can spend time with Maggie. T'Mir catches him and forbids him to make further contact with that woman, but Mestral counters that they must accept the fact they may never leave this world.
In spite of herself, even T'Mir takes an interest in the locals, as she learns that Maggie's son Jack is a very bright kid who desires a higher education but may not be able to afford it, even after his mom has been collecting donations in the bar's tip jar. The Vulcans are further drawn into community affairs when a coalmine accident traps at least 20 men underground. Mestral convinces T'Mir and Strom that they should use their technology to help, so by retrieving a particle weapon from the crashed ship, and with an assist from T'Mir's scanner, Mestral succeeds in rescuing the workers. Three months pass, and just as they've resigned themselves to living out their lives on Earth, they hear from a Vulcan vessel that will arrive in three days to rescue them. They inform their respective employers that they'll be returning home "up north." When Jack hears about it, he tells T'Mir he'll miss her, and reveals that he and his mom couldn't raise the money he needs for tuition, so he won't be going to college this year. Despite her own rule against getting involved, T'Mir retrieves something from the wrecked ship, travels to the big city, and sells it to a businessman — an "invention" that would later be called Velcro. She takes the money and anonymously stashes it in the tip jar devoted to Jack's college fund, which leaves Maggie astonished when she finds it.
As the Vulcans prepare to depart, Mestral announces he plans to stay — there's a unique opportunity to study an emerging species, one he's developed quite a fondness for. Stron argues the High Command would never allow it, but when the time comes to rendezvous with the rescue team, T'Mir covers for Mestral by telling the other Vulcans he was killed in the crash and his body cremated.
Mestral stayed on Earth presumably for the rest of his life, according to T'Pol. Archer and Trip question the veracity of her story, and ultimately dismiss it as a dinnertime entertainment. But when she returns to her quarters, T'Pol can't help but dig out an ancestral memento — the purse that T'Mir used during her time in Carbon Creek.