How do I melt the chocolate in a s'more?

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.

Edit: I didn't really notice any difference between microwaving the chocolate inside the marshmallow v. underneath the marshmallow.

I was recently on a canoe trip. We ran out of chocolate for the s'mores a couple nights before the end, so we substituted Nutella. No need to worry about melting, just spread it on the graham cracker. The resulting s'mores are much messier, though, since it all tends to squeeze out between the crackers.

Overall, we judged it enough of a success that we'll go straight to Nutella for future trips. It's just as tasty, much easier to pack and re-pack, and not a concern for premature melting in the summer heat.

There are two tricks that I know of:

1. Stuff the chocolate in the middle of the marshmallow. More time in the fire will help it get melty.
2. Roast your marshmallow long and slow so it's hot all the way through. It should practically fall off the stick. The hotter the marshmallow is, the more heat it can transfer to your chocolate. Let the whole s'more sit for a minute or two after assembly so that the marshmallow can warm up the chocolate.

Roast the marshmallow on a stick.

Assemble the S'more(s).

Put some foil on a rock by the fire and let them melt a bit longer.

Microwave the chocolate first in a microwaveable bowl, then heat the 'mellows and the crackers, before putting it all together. It's what I call "indoor s'mores".

Okay the best way to melt smores on campfire is simple. Years ago we would make campfire pies over the hot coals well this works great. place aluminum foil on inside so does not mess up your iron, lay graham crackers and choc precook your marshmallow and place on choc close up place back in coals for just a few min to warm up choc and you have best smores the way they are suppose to be melted and gooey !!!

For microwave smores, I top 1/2 of the graham cracker with a Hershey bar square and microwave for 30 seconds, then place a marshmallow on the melted chocolate and melt for a few more seconds (maybe 15 seconds), until the marshmallow increases in size. Then remove and top with the other 1/2 graham cracker.

I think Hershey changed something in their recipe to keep chocolate from melting too quickly in the sun/heat. Back in 1970 the chocolates melted just fine in Girl Scouts.