Tim's daughter Kathleen asks him if he'd ever killed anyone. She thinks that he must have because he keeps writing war stories. He tells her that he hadn't, but it's clearly a lie.
He tells us now that he killed a young man of about twenty with a grenade on the trail outside My Khe.
Or, in more detail:
The Alpha Company is at the ambush site outside My Khe around midnight. They are working in two-man teams, and Tim is on watch. He can see ten to fifteen meters up the trail.
All of a sudden, he sees the young man come out of the fog. There is no sound. Out of instinct and terror, Tim pulls the pin on a grenade and throws it at the young man. He's just trying to make the guy go away.
When it occurs to Tim that the young man is about to die (not just go away), he has to fight the impulse to warn him. Tim doesn't, and the young man dies, and his eye become a star-shaped hole.
Tim wasn't in any danger from the young man. The guy probably would have just passed him by.
Kiowa tries to help, telling Tim that the young man was dead even before Tim threw the grenade – someone would have gotten him.
None of it makes a difference to Tim, who can't stop reliving it and imagining a version of the story in which he didn't throw the grenade and the man lived.