2347

Events

The Setlik III massacre takes place, in which Cardassian forces raid the Federation colony on the planet. (TNG: "The Wounded")
Miles O'Brien becomes a transporter chief. (TNG: "Realm of Fear")
Ro Gale is killed during a Cardassian interrogation while his daughter Ro Laren is forced to watch. (TNG: "Ensign Ro")
Dr. Paul Manheim begins a search on a location that meets his criteria for his time and gravity experiments. (TNG: "We'll Always Have Paris")
To keep his son William interested and challenged in anbo-jytsu, Kyle Riker cheats at the martial arts during combat. (TNG: "The Icarus Factor")
Worf goes to live on Gault with his adopted parents Sergey and Helena Rozhenko and his foster brother, Nikolai. (DS9: "Let He Who Is Without Sin...")
Jason Vigo is born. (TNG: "Bloodlines")
Jean-Luc Picard pays a visit to his hometown La Barre, France. (TNG: "Family")

The exact date of the Setlik III massacre is unclear. However, we may assume 2347 to be the correct year, since Miles O'Brien mentioned it to have taken place about one year after he transferred to the USS Rutledge in 2346.
A Chateau La Barre was chosen by Jean-Luc Picard to drink when he returned home in 2367, however he mistook it for a 2346 vintage. (TNG: "Family")