Count me in with Buck on this one. On the PCT and the AT I had a GPS on my smartphone (just built in) but didn't use it much. On the CDT I bought and brought a dedicated GPS and was glad that I did.
To those that say "you don't need one" --- they're right, you don't, or at least shouldn't. But navigation on the CDT is indeed a much bigger challenge (it's mostly not a challenge at all on most other trails I've hiked on). That's not hype, that's just the way it is. Factor in also that if you're truly thru-hiking, then you can be certain to be spending considerable time in snow. More than the couple of weeks or so that I had considerable snow to deal with in the Sierras on the PCT (okay, to be fair, some in Oregon later on too).
I hiked most of New Mexico with a fellow who did the CDT with no GPS. This guy had a pretty strong set of direction skills and intuition and from talking to him I think he also had a few (more) cases of going the wrong way and then having to adjust/backtrack later that a GPS could have prevented.
It's possible it could be a safety issue. The vast, vast majority of the time not, but getting out of the south San Juans in Colorado I ended up quite high and in close-to white-out conditions. It was sleeting hard and even fairly well covered up parts of me were getting numb and I was wet through --- had to keep moving to generate body heat. So not having to mess around with navigation at that point was a very good thing.
There's also the issue of finding water in New Mexico. It's not something you want to get wrong, i.e., realize that the solar still you were relying on actually was that thing you passed a couple of miles back.
Beyond issues of safety and efficiency, there's also a certain comfort level in being able to get a quick fix and know for sure where you're at. It also made me happier and more willing to consider alternate routes along the way (Ley purple routes). The CDT offers a huge selection of alternate routes along the way.
It's certainly do-able to hike the CDT without a GPS. I was glad to have mine, and glad also to always have a spare set of (fortunately quite light) lithium AA batteries for it.
If nothing else, I suggest that you carry a smartphone with GPS capability and put something like Backcountry Navigator on there and spend the time to cache a lot of maps and put the (a) trail plot on there (the Ley plot can be found via web groping). As an aside, a phone/GPS that also can receive the Russian (GLONASS) satellites wouldn't be a bad thing for the northern parts of the trail, but probably not a big deal either.
The reason I liked having a dedicated GPS for the CDT was that I was using it a lot more, and could power it separately (AA batteries). This meant that it was always available, and I could still use my phone to blog daily, take photos, infrequently get a weather report, even read on occasion (it got dark early when I finished in Oct/Nov). Without worrying that I was using the phone battery so much that I would have to restrict GPS use.
Well, and also the GPS I went with was pretty weather resistant; if I use my phone GPS in the rain, I do so inside of a ziplock bag, with is a PITA. The standalone GPS I had was waterproof enough that I didn't worry about using it in any conditions.