There is a tree that is right above where the cars are Parked, causing some people I know to have to park their cars elsewhere out of fear the loose branch will fall and damage the cars.
It looks to be maybe 2-4" thick, maybe six feet long. About forty feet up the tree.
Is there any safe way to get it down or is it best left to a professional? What would a professional charge?
I’d hire a professional. A branch that size is heavier than you might think and can easily twist, bounce, and careen where you don’t it expect it to go. A professional will climb the tree, tie a rope round the branch, cut the branch, and lower it slowly and safely. So says my brother the arborist. What it costs depends on where you are, but figure a solid hour of work/pay if it’s easy and straight forward, transport and removal time, etc.
What’s a ballpark figure to have it done professionally? $200?
Is there a utility line anywhere close? If so make a phone call and the cost is zero.
You must have a different utility than us. Ours says they are coming right out but always waits until the tree falls over in the middle of a terrible rainstorm at two a.m. and kills the power for the whole neighborhood for days.
Ahem, I said the cost would be zero, I made no estimate of the timetable. 
What about your municipality? I saw a branch hanging over the road and called it in. They took it down within a day.
The tree is on private property and not near a power line.
Having done a bit of this type of work after some summer jobs on trail crews, I’d say hire professionals. 40’ is pretty high up there, you really need safety gear to operate at that height. And lowering a chunk of wood that heavy takes care. There are a lot of ways things can go wrong.
Call the city anyway. If people are avoiding certain street parking for it, the city might have a public works function for removing it. Even if they have a policy of billing homeowners, they should be willing to tell you how much. Then google arborists in your area and see if they’ll give you a quote.
I’d recommend you watch some tree-cutting mishaps on YouTube if you’re questioning whether it’s worth hiring a professional (or hiring even a rank amateur, but someone that is not you).
ETA: maybe start with this one
My town will come out and cut off a tree branch if it overhangs a street and they consider it a risk. That sometimes makes for some oddly shaped trees, but they don’t charge.
Check with the municipality, and speak with an arborist. Forty feet in the air is no job for an amateur.
Every few years, I need to get an arborist to trim my backyard trees. They grow quickly, and to the point where branches endanger my chimney, and the neighbor’s house. The cost is quite reasonable, considering the damage those branches could do to our structures in a windstorm. I won’t speak to dollar figures, since I likely get a lot more work done than you would need, and I’d have no idea how to break it down on a “cost per branch” basis. But like I said, it is reasonable.
Anyway, having watched the crew up high in the trees, with their special tools, and with their safety equipment, and with the way they lower what they’ve cut off so that it damages nothing on the ground, I’m confident in saying that it’s not a job for an amateur. What you are describing, OP, is better done by professionals.
I suspect a few of those folks did not survive their mishaps. 
Can you throw a weight over the branch? If you can, toss a weight with rope attached over the branch. Use the rope to pull a wire saw ($6-$12) over the branch and cut. Take the distal part of the limb first, then work your way back.
If this is daunting, call a tree service.
The tree is on private property, in a driveway. Not near the street, so I don’t think its an issue for the city/county.
Can people ballpark me on how much it’d cost to have it taken down, and where you’d find someone to do that? The people in question live in a small town, so I don’t know if a company would be local.
The owners should ask if their homeowner’s insurance will pay for it. Sometimes it will; it doesn’t hurt to ask.
I would look at “tree removal” and then explain I just wanted a branch down when I talked to them. At another house from my past there was a tree with some threatening branches. I called the local removal experts, they came and gave a quote for the branches or the whole thing, and we went from there. You may also want to check with some people at your local state/county/town parks departments; one may moonlight or be willing to.
Arborist? You people most live in fancy areas. We have tree cutters.
I’m sure policies can differ, but in my town if the tree isn’t on the township easement then they won’t do anything even if it’s about to fall on a group of nuns and orphans.
If you have a big, long rope you can tie a rock/weight on one end, huck it up so you get it around the branch, attach the other end of the rope to your bumper and drive away from the tree in a direction that will do the least harm, making sure no one is around.
Now if that doesn’t sound like something you want to attempt, then call a landscape/tree company, describe the issue and they should give you an estimate over the phone or come out and give you one. They’ll likely just need a bucket truck and will have it down safely and quickly. Those type of stuck branches are called “widow makers” for a reason.