The 2010 Bungie game that preceded 343 Industries taking control of the Halo franchise was Halo: Reach.
Released for Xbox 360 on September 14, 2010, Halo: Reach is a prequel set shortly before Halo: Combat Evolved. Players control Noble Six, a Spartan serving with Noble Team during the Covenant invasion of the human colony Reach.
Reach was Bungie's final Halo game. Although 343 Industries worked with Bungie on some post-launch content, Microsoft created 343 Industries to oversee future Halo projects after Bungie's departure. 343's first major project was Halo: Combat Evolved Anniversary, released in 2011.
A common mix-up is Halo 3: ODST, which was also developed by Bungie but released in 2009. Destiny came later as Bungie's first post-Halo franchise, while Halo 3 was released in 2007.