The key for the chest is in the other tower, in a small chest on the uppermost (IIRC) platform.
To get to the chest, jump over to the last section of the ramp, then jump for the first beam where it meets the wall; if you overshoot a little the wall will stop you. Save once you make it there, then turn towards the next beam and jump over to it; move slightly forward and then jump, but don't keep the forward button / stick direction pressed the entire jump, or you will go past your mark (I had to reload several times here). I kept close to the wall, as the beam was slightly thicker there. Once you reach the second beam, save again; getting to the chest is fairly easy at this point, but if you miss the timing on moving forward and jumping, you can fall off rather than jump (umm, so I've heard). A high camera angle may help getting the timing and positioning correct (ie to make sure you have room to move forward as you jump).
For all that effort, though (I jumped over to the chest before I had the key, so had to do it again), the only thing I got in the chest was a couple potions, and the book was not unique (don't know if it is random, but I got the 'life the universe and everything' book, which was great, but I had seen it before).
Welcome to the forum.
