He died when Jade (Jessie's Girlfriend) took a gun from the detective and shot him. Tiffany (Chucky's wife) also stabbed him then he came back and stabbed her.
No chucky doesn't die. His son/daughter chops off his arms, legs, and head. Then later in the movie when glen goes to open his present he finds chucky's arm. So I'm guessing that he's still alive. So...