I haven't used the one Vaskania posted a link to, but I have it. It might work for what is needed, but if not, I use Mesh:Vertex Tools for this sort of work, and it works great. The only caveat is it is an older add-on for 2.5x series, but I use it exclusively in my 2.71 setup. I can't attest if it will work in a version past that, though, it might. The good thing is all past versions are available for download, and you can use them side-by-side with no issues. If you are working in current version, or later version, you can append your work to 2.71 if you can't outright open the newer file in older version.
Here is a quick mini-tut illustrating work-flow:
1. Select mesh, and go into Edit Mode. Next, select Vertex mode. Now, select all verts. Following image illustrates your issue:
2. Press CTRL + V to bring up the Vertices Menu. Then select "Distribute" in the Vertex Tools Section. It will distribute all vertices evenly along the loop creating even edges that you need:
3. No other steps - you were done at step two. Here is the result with even edge lengths:
4. Here is the add-on in User Prefs:
You can get the add-on here:
Blender Addon List: Addon: mesh vertex tools