Sigmund Corp. uses a technology that can create artificial memories. They offer this as a "wish fulfillment" service to people on their death beds. Since these artificial memories conflict with the patient's real memories, the procedure is only legal to do on people without much time left to live.

Sigmund Corp. employees Dr. Eva Rosalene and Dr. Neil Watts are tasked with fulfilling the lifelong dream of the dying Johnny Wyles. Johnny wants to go to the moon, although he doesn't know why. The doctors insert themselves into an interactive compilation of his memories and traverse backwards through his life via mementos. With each leap to an important moment in Johnny's memories, they learn more about him and what brought him to his current position in life, including his largely unhappy marriage to his childhood sweetheart, River. Upon reaching his childhood, the doctors attempt to insert his desire to go to the moon. Supposedly, Johnny's mind would create new memories based on that desire, and Johnny would die believing he lived without any regrets.

However, Johnny's mind does not create the new memories as planned. Dr. Watts and Dr. Rosalene must solve the problem to fulfill Johnny's dying wish of going to the moon.

Eventually, it is revealed that Johnny and River met as children at a carnival. They looked at the night sky and made up a constellation: a rabbit with the moon as its belly. The two agreed to meet at the same place the following year, with Johnny promising that should he forget or get lost, the two would "regroup on the moon". That night, Johnny gives River a toy platypus which River treasures for the rest of her life. Shortly after, Johnny's twin brother Joey was killed in an accident. Johnny's mother gave him beta blockers to induce memory loss of the tragic event, also causing him to forget his first encounter with River. He later happened to meet her again, and eventually marry her, and River only realized later on that he had forgot their meeting at the carnival. (Johnny confessed that he approached her in school because she was different, and revealed that he thought that was their first meeting) River, diagnosed as an adult with Asperger syndrome (although never directly stated, the game references Tony Attwood, who wrote numerous books about Aspergers), did not tell Johnny directly about their first meeting; instead, she tried to indirectly jostle his memories by cutting her hair and crafting paper bunnies, including a dual-colored one representing the constellation they made up during their first encounter, combined with the blue-and-yellow dress she wore on their wedding. River was unable to make Johnny remember before she died, and Johnny was left with lingering guilt and an inexplicable desire to go to the Moon.

In the present, Rosalene and Watts eventually implant a memory sequence in which Joey did not die, and lived on to become a popular author, and Johnny did not meet River again until they started working together at NASA. As the comatose real-life Johnny begins to die, he imagines going on a moon mission with River. During the launch, River holds out a hand to him. The moon appears through a window on the ship, and Johnny takes her hand as his heart monitor flatlines.

In the epilogue, Johnny and River eventually get married, and build and retire to the same house where the real-life Johnny and River lived. Back in the real world, Rosalene and Watts look to Johnny's grave, which is placed adjacent to River’s. They reveal to the audience that Johnny willed the house to his caregiver, Lily. Rosalene receives a phone call, and the two move on to their next patient. While Watts is leaving, he stops and the screen briefly flashes red, the same way it did when Johnny felt pain. Watts takes some painkillers, then continues onward.