I had it really bad in both elbows. From beginning of symptoms until now where I'd say I'm virtually symptom free outside of intense pull-up or rope climb WODs, it has been 2+ years. I did a ton of research on the net and I found that not just one approach fixes everything. I did the following at the peak of my symptoms where both elbows basically ached all day long:

1. Take a good amount of time off from any WODs with pulling. Pull-ups, Rope climbs, rows, etc. It took about 2 months completely off of Crossfit and another 1-2 months of no pulling exercise. Then I started back with heavily scaled activites (i.e., big band assist on pull-ups, still no rope climbs, etc). It REALLY sucked to take this much time off but it was best for me. I couldn't go into the box without getting sucked into the mindset of "oh I can just tough my way through this workout even though I know my elbows will hurt from it".
2. 10-12 sessions with a myofacial release expert. Ask around your box as most experienced CF'ers seem to "have a guy".
3. Nightly streching for 10-15 minutes of both forearms plus 2-3 minutes stretching sessions a couple of times each day. This can be pretty painful but it does help.
4. Wearing a golfers/tennis elbow brace for every WOD. I'm down to wearing just one of my worst elbow now. This helped ALOT and I'll keep wearing it until I'm 100% symptom free. I think this is a must. Not all of the braces are the same so try several and find the one that works the best for you. I think I have about a half dozen different kinds of elbow braces.

It sucks, but with the stress you place on your elbows in many of the WoDs, don't think this will just go away. You'll need to work aggressively at this or it WILL become chronic.