I have net framework for 64 bit systems and yes it works.
I can Open the Editor just on Screen but cannot do anything with it.
Just does not work... no error message I remember when I tried it several times.
I do not have CIV IV... yes CIV III/Conquest Runs Great.
I also have XP Professional x64 Edition, and unfortunately ran into a similar problem. It takes about 10 seconds for your editor to load (compared to instantaneous on regular XP), and it uses up to about 320 MB of memory in the process, shrinking to 90 MB-ish after it loads (regular XP it stays below 50 MB throughout). At that point, everything looks okay, but trying to open a file which works on regular XP fails. I got an error message "The current max icon index for units is 1471. But the current Unit32.pcx file contains only 0 images." I've checked and the file seems to be there and not have no size, although it is called units_32.pcx instead of unit32.pcx (not sure if that has anything to do with the problem, but probably not as it opened fine on XP 32-bit).
Civ3 does work on XP x64, and seems to work well. My initial speed tests showed it taking about 40% longer for the AI turn on my usual test save file, but I am not certain I didn't make an error when setting up the test (i.e. forgetting to turn off a setting I usually turn off). As for 64-bit Vista and Win7, my sister has had no problems running Civ3 on Vista 64-bit. I can't get it to agree with any Vista or Win7 installation I put on my laptop, but it is possible to have a Vista/Win7 64-bit installation that will like Civ3 and play it just fine.
It would be nice to know if Vista/7 64-bit run the current version well. If they do, it probably isn't worth creating two versions.
Somewhat more on topic, I was playing around with a hex editor and changing Civ3's memory space as it was running last week, with some success. I wonder if such an approach would be at all feasible? I see two major pitfalls, one being that I suspect it would be much more difficult to program, and two that graphics may present a major issue when it comes to dynamically changing them (not counting the documentation issue). But for changing information that was stored in the copy of the BIQ in memory, it did work quite well (ex. changing the cost of a Barracks from 40 to 100 shields showed up as soon as I saved my changes and moved the cursor in Civ3).
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Yesterday was my 64-bit Vista Ultimate
I believe it would be a good Idea to have others try it with their 64 bit systems because there could be some difference for my system. 
