Wow, thirteen weeks. Darn, I replied to mudpuppy instead of you (I keep doing that!) and now I can't see your profile. Where are you located? You might want to consider herding training, too, as it sounds like he's got some strong instincts!
So that's the good news, you've got a real live Border Collie there. That doesn't mean, though, that he "has" to chase cars. So don't feel like you are in a hopeless situation. Think of his mom and dad - if you saw them working, you would have noticed that they had the ability to be around livestock (sheep?) without chasing them every second.
But, even though that ability is in him, you gotta teach him how to use it. It's going to take a while, so go find your "patience" hat and stick it firmly on your head! 
Step one - as mudpuppy said, keep him away from the lure of traffic for a little bit. Honest, play your cards right and this will only take a couple weeks. Puppies that young don't need tons of exercise - just pretend he's got a life threatening illness and it's up to you to cure him. And, if you think about it, car chasing is potentially lethal, right?
Step two, teach him something to do instead of chase that car, when he hears/sees the car. First, teach him to "down" no matter what. He already knows it, you say, but does he really know it? Down means down even if you are running around, somewhere else, etc. He may think down means "come and then down" - you can teach him not to do this by saying, "Eh-eh! OFF- Down!" and sort of pushing your arms at him like a crossing guard.
Clicker training is really great because it helps a dog know they did something right RIGHT THEN and not when your hands get to the treat and give it to them. It separates "capturing" the behavior, from the actual reward - "good boy" can muddle things up for a dog that works for praise. My Coltrane is like that - you have to mark, then praise, because it's so rewarding to him - better than a treat. If I don't have a clicker, I just repeat the command in a "happy calm voice."
Anyway, get him to where he's really comfortable with the down, and then start phase three. You need to be really alert for this. Go to where the cars are audible or visible, but not right there (like a park where he can see traffic far off). Watch for the signs that he's getting excited. remember to stay calm, breath calmly yourself, be alert but make sure you don't have a death grip on the leash.
Watch for him to look at a car, move his ears forward a bit, pant a bit. Ask him to lie down, then praise him very calmly. Don't throw a party - you want him to stay calm! But talk to him quietly.
Don't push it. Walk away, still telling him what a good boy he is. Then turn around and walk back to the place where he was starting to react. The moment you see it - ask him to lie down. Tell him he's a good boy. He's allowed to watch those cars, just as long as he's laying down doing it.
If he won't lie down, tell him, "Sorry!" and turn around and walk briskly away, then ask him to lie down again. Praise him when he complies. Next time don't go so close.
That's the cool thing about this. He'll tell you when he's comfortable doing this, and when he's ready to go forward. It's a bit like "simon says" and he is "simon". If he fails, don't get discouraged. He's just telling he needs it to be easier. Sometimes where he fails won't make a bit of sense. Don't worry about that. Your job is to make it easier to obey, his is to tell you when it's too hard to obey.
Gradually it will get easier for him, and you can go closer and closer to the road, until eventually you'll be able to safely stand in the middle of a busy intersection, or even ask him to DOWN if he's off leash accidentally near a road.
That won't happen overnight though. Remember that a puppy's brain goes through many stages and there's several points where his brains will fall out his ears, and he'll seem to have forgotten everything. Don't get upset or discouraged. Pretend, emotionally, that you've never seen this dog before in your life (and in a way it's true, Border Collies go through such rapid changes mentally that they can seem like totally different dogs at various stages!). Continue to follow his cues and go back to where he CAN obey you, each time he has a meltdown. "Disobedience" is not wilfulness or rebellion, it's information that you can use to figure out your dog's needs.
You'll have to trust me at this point when I say your efforts will be well rewarded, even if you don't see it for many months. There's a point after adolescence, at between 14 and 18 months, when it seems like a switch is thrown in your puppy's brain, and suddenly he knows everything you've working on - and a year after that you'll have a hard time remembering all the work you had to do to get where you are!
Good luck!