To repeatedly dream of being chased suggests there is something in life you are trying to avoid.

The fact that someone is trying to kill you can be interpreted several ways. Maybe it signifies the degree of fear regarding whatever you want to avoid. Maybe it is more about the degree to which you are actually avoiding something - as though you are 'killing off' a certain part of your own emotions rather than deal with whatever is bothering you subconsiously. Death can also signify an ending or significant change. Whether of a way of life, a relationship, or a way of thinking.

Is there some big change in your life that you don't want to face? Or something else that is worrying you?