I just finished my BSN at Chamberlain (I got my ADN at a community college in 2006). I have a good job, and none of the brick and mortar grad schools I'm applying to have said anything negative about Chamberlain. Chamberlain is fully accredited at most locations (the newer ones aren't yet, because no new school starts out accredited, but they surely will be). No one cares what school you went to, or even what your grades were. I have only ever been asked to show my nursing license (my first job wanted a copy of my diploma while I was license pending, but they did not care what school it was from). That being said, though, my advice to you is to go another route.
I think Chamberlain is fine to get a BSN if you already have an associate's degree or diploma in nursing, but it is far too expensive in my opinion to be an option for entry into nursing, unless you're desperate, but in this nursing job shortage, no one is THAT desperate! It's a good school, it really is, but it's very expensive (my rule of thumb is that you shouldn't pay more for your entire education than you'll make in a year, and getting your entire education at Chamberlain would violate that rule - getting your ADN at a community college and then the BSN from Chamberlain wouldn't), and like another poster said, you need to get the full college experience. You can't get that at Chamberlain. You are young, and nursing is too stressful to give up the fun you could have at a regular school. Honestly, nursing is my second career, and I wouldn't trade the memories I have from my university days for anything. I can't tell you what to do, and Chamberlain is a good school, but you really might want to explore less expensive options and give yourself a chance at having the full college experience.