Since you specified not wanting any equipment other than a campfire and a stick, the best I can do is add one more piece of equipment you should be able to find anywhere (i.e., not have to carry with you): a rock.
If you put a flat-topped rock just to the edge of your campfire, you should be able to place a graham cracker and slab of chocolate on top of it. While you are toasting your marshmallow on the stick, the chocolate should start to melt. This technique won't produce totally melted chocolate (unless you have a very large, very hot fire), but the chocolate should get a little melty without being so runny that none of it makes it into your mouth.
This only works if you have thin Hershey bars or other chocolate in relatively thin pieces. Thick slabs won't soften all the way through with this type of indirect heat.
And for those people concerned about dirt, bring some aluminum foil to act as a buffer between the rock/dirty stuff and your s'more.
Extraneous but related note:
Your question got me thinking about ways to achieve melted chocolate with microwave s'mores (a last resort if I'm stuck inside with an electric oven or no oven at all), and I have an idea I'll test out tonight. When I microwave s'mores, I usually microwave the bottom graham cracker, chocolate and marshmallow together, then top with the other graham cracker once the marshmallow gets gooey. The chocolate doesn't really get melted that way, though, because marshmallows take almost no time at all to melt. I'm wondering if pushing the chocolate inside the marshmallow before I stick it in the microwave might help the chocolate melt more. I will update once I've had a chance to try this.
I didn't really notice any difference between microwaving the chocolate inside the marshmallow v. underneath the marshmallow.