I recently picked up a Remington 700 7mm RM in a trade and noticed that it is very hard to chamber ammo for. Even new cases (that I FL resized) require a considerable amount of effort to close the bolt on. Upon visual inspection everything looks fine.

Any ideas?

Take it to your local gunsmith. He will check headspace, pour a chamber cast, check extractor and ejector. Why chance it?

I am already planning on taking it to the gunsmith, but I was just hoping to have a few people venture to guess what it might be before I take it in.

The strange thing is that once I get the bolt closed on a case I can raise the bolt then lower it again with hardly any effort. However if I eject the case and try to close the bolt on it again it takes a lot of effort the first time I close the bolt again.

My first guess would be an extractor problem.

Since I have posted this I have messed around with the rifle a little more. I have since discovered that it has the most trouble with Winchester brass - virgin or full length resized brass. Remington brass feeds better but is still harder to close than it should be. Federal brass on the other hand feeds about like it should feed. I have taken measurements of the brass and noticed that the belt on Federal brass is 0.528", the Remington 0.529", and the Winchester 0.530". Those are the only measurements I can tell that are "smaller" on the Federal brass than the other two.

Your on the right track, but the wrong area. Check the rim (behind the extractor groove) for both diameter AND the amount of bevel at the outer edge.
The 700 has to force the extractor ring over the rim, this is what your feeling.

I'll second Tailgunner on this one. I experienced hard chambering of Blaser CDP factory ammo in my rem Sendero .300 Win., while other ammo, factory or handloaded, chambers easily. After checking everything out, I noticed the bolt head recess to be on the small side, while the CDP's RIM (not belt) was on the large side. Check for rubbing marks around the rim.