I would say you have a solid chance if 1) You finish all of your applications and make sure they are in the hands of the admissions committee before mid-February (call them up, e-mail them, visit them, do whatever you must to make sure they received everything before the deadline) 2) apply to schools that are realistically within your range plus a couple reach and a couple safety schools.
Applying later is definitely a disadvantage. I tend to think that people who apply last minute and scramble to put everything together generally submit a poor quality application (because they rushed) and aren't really as committed to attending law school as they should be. Attending law school is a lot different than college. Law school is a 24/7 job in many respects, and it's breaks you down and changes you forever during your first year. It's also a long-term career and lifestyle choice. Once you come into law school you can't really change your mind and quit because you would have accumulated massive debt and probably re-located, too. This is all just food for thought. If you have additional questions, message me.