I do... in an indirect way. I used to be a systems administrator (dealing with server and clients) then was a network admin and now am a security admin, but I still do a lot of networking. In all honesty, I don't know what Chubb is. Enlighten me?
As for education, getting a cert is very useful right up front. Network+ is a start, and your CCNA/CCNP is also very, very useful (it's what I look for when hiring people). Also, many companies are slowly getting on the bandwagon, regarding IT, that experience trumps education. It USED to be this way a long, long time ago, then changed, but is changing back. A CS degree won't help much with networking, per se, but a degree is an in at a lot of larger companies still (especially if you don't have 10+ years experience). There are some schools that offer speciailized progams (Chubb may be one?) such as ITT Technical Insititute or, here in Arizona, The University of Advancing Technology (
www.uat.edu) which lead to associates or bachelors degrees (UAT even offers post-grad degrees in some fields). However, experience is paramount. Intern hard and intern often or just get a part time job working with computers. It doesn't HAVE to be in networking either. Get a job at Best Buy as a bench tech (that's how I started, though at a small local OEM since Best Buy was no where near me back in 1994). In fact, if I could live on that money, I'd go back to being a bench tech again. There's something wonderful about just tearing things apart, and you ALWAYS get to see the latest and greatest technologies in action.
For network specific experience, try to work as an admin at your school of choice. They'll all have computer networks, and most are at least partly run by students. This is great experience and looks awesome on a resume.
Where are you located? I can answer a bit better knowing that. I hope this has helped...
~X