You don't need to use a choke chain however I understand why people do - they aren't barbaric but given the breed, may not work.
I'd suggest stopping and being patient, let your BC know that you only move when you want to - not the other way around. The Halti face harness as Paddywak suggest is, in my opinion, a safer and quicker way of training. Using clickers (similar to what AlwaysConfused suggest re training) is also a good idea since Border Collies are very smart - as AC has said.
Every single one of our dogs used to pull on lead and I've adopted all suggest above to work successfully.