Does Islam allow men or women to remove chest hair?

First as in many religions, there is no one "Islamic" belief, there are many groups within Islam and for some rules vary. So you really need to first clarify what group you are with and where you are at.

The issues for women, is that of purification, and from my understanding normally they should regularly keep their body (except head) free from hair. Also the issue of following the rules of their husband.

But you need to clarify with your local religious leader, as to your groups rules.

Please open the links below you may find your answer, Thanks.

Sheikh Hatem Al Haj :: QA Section :: Acts of Worship Character New Other :: Can a Muslim male shave his chest?

http://islamqa.info/en/9037