Wow! A 65 Dart! Does it have the push button shift on the dash and a genuine slant-6? A girlfriend in my distant past had one of these and it was a blast and a half to drive. No matter. Most newer paints are acrylic, which is a plastic of sorts. You need a remover specific to the type of paint used. Your problem is that you may remove more than desired. Chrome is mostly inert. Chrome forms an oxide layer which very tight, cohesive, and once chromium-dioxide forms on the surface, the oxide separates teh base metal from the environment, which is why it stays so shiny. The layer is very thin, but very passive, very non-reactive even though it is only a few molecules thick. Look at stainless steel. It is the chrome added to the iron which is what makes it stainless and not rust like any other iron. Anything you use which can attack the acrylic paint may also affect this oxide layer. Visit a local auto body shop which repaints vehicles. They will likely have a solvent which will remove an acrylic paint and NOT touch the oxide. See if there is some way to remove the emblems. Most emblems of the day were pinned in place. They used one or more rods on the back through a hole with a spring clip pushed down on the rod to hold the emblem in place. The reason for using this type of fastener was the spring part would hold the emblem tight to the surface. Each has at least 2 rods, so as to maintain alignment which is not possible with a single rod, but usually, only 1 of the 2 rods is clipped. Unfortunately, you have to break the spring clip to get it off since it is a one-way device, so you will need replacements which you can probably find at any repair shop which does body repairs rather than whole panel replacements. When you go to break the clips, be very careful since the rods are relatively soft and are easily broken off instead of the clip. The easiest way I found was a pair of needle nose pliers to get under one edge of the clip and twist upwards which flexes the clip and snaps it instead of snapping the rod. The other way is to treat it like a nut and "unscrew" it while pulling up so it literally cuts threads up and eventually off the rod, which damages the rod, of course. Your worst case is if they peened the rods like a rivet in which case, you will end up grinding off the rivet head to release the emblem and then you will face the problem of refastening later. Whichever way the emblems are fastened, you have to remove them so you can get the paint off without damaging the surroundings of where they are mounted. Good luck. A 65 Dart is a classic and deserves doing the job right! Back in the mid 60's, Revell Models sold several visible engine models, V-8 (a big block Ford), Pancake 4 (Corvair), Slant 6 (Dodge) and the oddball, a 9 cylinder Allison radial aircraft engine. Each had transparent block parts so you could see the internals move as you turned the crankshaft. I had them all. If you have the slant-6, you might consider trying to locate one of these model kits, maybe on Ebay.
Edit: I just saw a few others posted before I did and one suggested steel wool. I would advise AGAINST using any kind of abrasive. Any abrasive will get the paint off, sure, BUT will also damage that oxide layer I mentioned which is a very BAD thing. If you decide to use steel wool, get the finest you can. No "brillo" pads. Steel wool works by using very sharp edges on the ribbons of steel to literally scrape the surface, much like a razor does to shave and like a razor, can damage the surface which lies under what you are trying to remove. Don't get me wrong, it WILL work to remove the paint but it may also damage the oxide layer and you will lose the shine of the chrome in the process. Just be very careful. Your best bet is a paint remover rather than anything abrasive.