In virtually all jurisdictions, you are allowed to prune the portions of a tree overhanging your land, at your own expense. Those limbs, after all, are occupying your property and you have domain over them -- or under them at present. And yes, your trimming rights even apply to heritage trees, but with a few minor restrictions that I am pretty sure you can comfortably meet.
Heritage trees, by the way, are large individual trees that have some kind of noteworthy characteristics that merit preserving, such as age, size, circumference, rarity, ecological value or historical status. Some have served as longtime landmarks, while others have even had key treaties signed in their shade, though that's probably not the case with yonder mighty pine. ("I'll be glad to sign the treaty but first, why the sticky exclamation point made out of maple syrup? Oh ... pine sap.")
Typically, a permit from the city or county is required only to remove or heavily prune such a protected tree. Since it's doubtful that your intent is to heavily prune -- whacking back a quarter of such heritage trees is typically the limit -- then you can proceed.
But at least be cordial to your neighbors as you plan this. Make sure you inform them well in advance of your plan. They may want to quickly even out the prune job after you take a bit off the side. In a perfect world, you could coordinate this on the same day. For added peace of mind, you might want to contact your homeowners insurance agent before you go all "Clark Griswold" on the pine and ask them if you are proceeding correctly. The odds say you are. Your neighbor may protest but can't interfere with your property rights. Ideally, though, you'll be extending an olive branch to gracefully remove a pine branch.
If you do prune the pine, be sure it is done at the very edge of your property in a straight line from the ground to the sky. For good measure, take several before-and-after photos from different angles to show you have trimmed only your side.
I can't say I blame you for not wanting a sticky, speckled mess of sap on your car that at first blush looks like your vehicle is a bird perch. So gas up that chainsaw or better yet, hire a professional to do the job, budget willing.
The moral of this story: You don't want to needle your neighbor, but you don't want to play the sap either. Good luck!