OP, I'm very happy for you that you're in remission. That is no small thing to deal with, and it says a lot about your character.
As to your specific question, no, I don't think it will hurt your chances for admission one bit. If anything, it shows incredible determination and fortitude on your part, both of which are highly desirable traits in a law student.
On a side note, my cousin was diagnosed with stage 4 metastatic cancer. He was told that it was especially aggressive, and his chance for survival was slim. He beat it, it came back, and he beat it again. That was nearly 20 years ago, and he's doing just fine. There are many people out there who are beating the odds every day. Best of luck to you!