Law schools tend to use "rolling admissions" which basically means that the earlier you apply, the better your chances. So you've got the right idea when you ask "how early is early?". A good goal is Thanksgiving. I think most of the schools have a "first day" that they will accept applications, maybe in October? You'll have to keep checking the schools' websites to find out exactly when they will accept applications. Sign up to get the little brochures from all the schools that you're interested in. They sometimes explain more than the websites and they're nice to look at.
The trick to getting applications done fast is to make sure to get the ball rolling on your letters of rec., transcripts, etc., as soon as possible. You can always stay up all night filling in the blanks, but you can't force your professors to write those letters. Look at last year's application and make sure you have everything you need, next year's won't be too different. Get started on your personal statement, it can take a while.
As far as chances go, there is a website that tells you the odds based on last year's applicants' numbers. I found it once for someone on this board and I don't have time to look for it right now, but it's on the lsac.org website (read some older posts if you want to find the link). Bear in mind that times are changing and last year's odds might not reflect next year's odds. The class of 2005 will likely be much more competitive than 2004, but 2006... its up to you to speculate. Apply to a range of schools and keep in mind that anything can happen. I think a lot of people this year were surprised that they didn't get in to schools where they had comparitively high numbers, they were competing against a much larger applicant pool and everyone was better qualified.