I'm sure that with all the openings out there that there are novelty moves and variations in those openings that haven't been discovered yet but as far as an entire new "good" opening system, I would say highly unlikely.
Is it possible that there are still good openings that remain unexplored?

I don't think that there are any entirely new openings out there but no doubt there are some good variations still to be tried, or taken further.

@jshpwll
"Depends on where you draw the line..." I agree. Other than that I believe every opening that gives good chances for a win on both sides has been analyzed by now. Super GMs often only play certain openings including the Ruy:Berlin,QGD, NID, Grunfeld,Sicilian, and the occasional English because everything else is often lost at that level.

What about defenses? I also think it would only be possible to see all of the potential successful openings with computer analysis. But I think computer analysis is flawed. It's not a very good inventor. If Fischer hadn't gone crazy I think he would have made a few new ones work in his lifetime.

What do you call your opening against mountvernon427? I cannot believe your 7th move - you could have pushed it one square more! ;)

Chess is vast and we have explored only a small part of it. I expect, as time goes by, that more and more positions now thought "unplayable" will be re-examined and make their way into regular tournament practice.
There are also whole openings yet to be thoroughly explored. 1. Nc3 is a common opening in Correspondence chess, yet rarely appears in OTB.
There may also be mileage in moves like 1. d3, 1. c3 etc. I can set my computer to play either of these as its first move, and I always lose. Not that means a whole lot. It outgrades me by about 1000 points. I can make it play 1.h4, and 2. a4 and it still beats me.

I agree with post #12, 1.Nc3 seems to be the only decent opening that has not been heavily analyzed. I would not call 1.Na3 or 1.Nh3 decent.

Nh3 followed by g3 is surely playable?
This is an interesting question. I don't know very much about the King's Indian Attack, but it seems like the moves you suggest might be able to transpose into a reasonable line in that opening. If so, I would agree with you that 1.Nh3 ... 2.g3 is a decent opening.

The beauty of chess is how vast the possibilities are- even modern computers struggle to calculate the total amount of variations in any given game.

1Na3 2 Nh3
Well, 1.Nf3 ... 2.Nc3 ... is the "White Knight's Tango" (the colors-reversed version of the "Black Knight's Tango" 1...Nf6 2...Nc6).
So I guess 1.Na3 ... 2.Nh3 ... might be called the "White Knight's Salsa".

Nothing, at the moment, especially if your opponent is stronger than you. You can then learn to defend a difficult position. But if you open all your games like this (white and black) I predict that you will have lots of similar games where you are defending for 50, 60 moves and then still lose without ever getting any of your pieces in the other half of the board. Some people would find that boring. Try it for a few games, maybe 5 or 6. Then try something else for a few games and see which system you prefer playing. How about starting 1. e3, 2. c4 and 3. Nc3? You follow up with d4 and Bd3 (or Be2) in most cases. Some games will have you on the defensive, some will let you attack with f3, g4, h4 etc. You can also play this sort of thing with black. Good luck!
...or is there truly nothing new under the sun?