How to handle a difficult coworker

I need some recommendations on how to deal with a difficult coworker. I work in a startup of sorts and dude joined in and from the start had a habbit of brown nosing every person in spotlight. Recently he started with me. He props me up infront of others but then also backseat code my tasks as well and pretend that he did better than me or was the first one to do it. Always jump in things assigned to me and try to show off. Its getting to the point that is unbearable. Any suggestions