According to Scoringsessions.com, John Williams has begun scoring Star Wars: Episode VIII today. It looks like he is recording the bulk of the score in the spring, however. With Williams starting this early, he could be scoring the music to the first trailer right now.

John Williams starts recording music for STAR WARS: EPISODE VIII at Sony today. The bulk of scoring will be in the spring. — ScoringSessions.com (@scoringsessions) December 13, 2016

Star Wars: Episode VIII hits theaters December 15th, 2017.