In this context, "chase", "pursue", and "follow" all mean the same. In other contexts, "chase" and "pursue" mean to go after something, and usually that the peton who "chases" has the decision or lead. "Follow" means that something else is leading you--a person, a dream etc. It usually implies the follower has less decision and action.
While all three are correct and native english speakers can be heard saying all three, the words change meaning slightly based on connotation or what that word is usually used for. Chase has a wilder meaning, it makes people think of a police officer racing after a criminal or a mother running after her child. In this case, it implies you are passionate and wild about your dream (in a good way). Pursuing is less crazy, more deliberate and serious. Following is a neutral verb and is the most common word used with that expression. Despite this, all three work quite well.