Is there a (flavorless) chemical that be added to water to create carbonated water?
Yes, carbon dioxide.
A bit more practically, if you want something liquid, then you can add carbonic acid, which decomposes into carbon dioxide and water.
In either case, though, it’s not going to be flavorless, because carbonic acid has a flavor, and if you add carbon dioxide to water by any means at all, some of it’s going to convert to carbonic acid.
What Chronos said.
Easiest way I have seen it done at home is to plop some dry ice into a glass of water.
That said I have not seen dry ice up close in 30 years. Seemed to be you could buy it at a store when I was a kid (at least can’t imagine where my mom got it except there). Dunno where you’d buy it today (not that there is anything weird or restricted about it…just not in your local supermarket).
I buy mine at Acme Ice, just down the street. 
It’s great for packing ice cream up to mountain summits on the hottest days of summer.
Around here (Modesto, Ca-area), there are supermarkets that carry it.
Heh…cool (no pun intended).
I have had no need of it so have not asked at supermarkets I visit. Just never seen a dry ice section when wandering through.
I guess we should add a disclaimer to anyone interested to be careful with the stuff. Pick it up with your bare hands and you can lose some skin pulling it off (yes, I learned the hard way when I was a kid ).
I might ask at my local market…I have no need of it but the novelty is fun.
I found dry ice at Hy Vee. A teaspoon size piece does about 2 liters of liquid. Don’t blowup the container as the pressure builds.
They don’t have it out on the shelves where just anyone can put it in the cart, but the Albertson’s around here has a sign on the ice freezer saying that you can ask for it.
Our local supermarket it (Fred Meyer) has it in a locked (and chained!) freezer. The freezer is covered with warning labels and you need a store manager to unlock (and unchain it) in order to buy anything.
While that might be a bit overly cautious the stuff is slightly dangerous. It is very cold and kids are in stores and even adults may not be aware of the hazard it poses.
Not trying to overstate the hazard but as I mentioned I lost some skin when I was a kid when a grabbed the cool looking smoking piece of ice. No biggie in the scheme of things, no permanent damage or anything requiring a hospital visit. It did hurt though.
Now I think about it I think it makes sense for stores to keep it out of easy access and make people ask for it.
Is that where you can pick up jet-powered skates and giant rubber bands, too? 
I seem to remember being told you could make fizzy orange juice by adding baking soda. We eat the stuff all the time, and specifically use it to create carbon dioxide bubbles, so it should be safe.
I’m pretty sure that, on Good Eats, it was said that getting baking soda wet would create bubbles, so that seems like a possible solution.
I have a chemistry degree, and I’ve never seen bottles of “carbonic acid” for sale, not even in the chemical suppliers’ catalogs. I’ll buy that method as soon as you can show me where I can get that bottle of carbonic acid. In fact, it’s more than likely that what has been dubbed as “carbonic acid” really is hydrated CO2. Link
You’ll need a little bit of acid as well. When you’re baking with baking soda, the acid usually comes from some kind of soured milk product like buttermilk or sour cream. And if you add too much baking soda to your fruit juice, it’ll probably taste funny since you’re neutralizing the acids in the juice.
Fizzies, like Bromo-Seltzer likely contained a mixture of sodium bicarbonate and citric acid.
Toss a couple in water, and you’d get sweet, flavored, fizzy water.
There’s a gizmo called the Soda Stream that infuses water with CO2 to create carbonated water. It’s pretty popular in Germany, but then we tend to drink a lot more carbonated water than 'Merkins. You can add syrup to it and you’ve got lemonade, cola or anything else you like. You can even refill (or exchange) the cartridges in pretty much every supermarket.
Just out of curiosity, what do the refills/exchanges go for? One the major criticisms I have for the SodaStream in the USA is that it’s proprietary and can’t be refilled at market rates, meaning that you’re stuck with overpriced, propriety refills. I use my beer serving system… my last 20 pounds of CO2 only cost me about $18.
A refill/exchange (you exchange an empty cartridge for a full one) is about 6€ and is enough for about 60-80 liters of carbonated water, depending on the desired strength of carbonation. A bottle of carbonated water, generic brand would cost you about 0.40€-0.50€, and you have to schlepp that stuff home, so 0.10€ is a pretty good deal, if you ask me. It is, however, proprietary, but there are only about two brands to choose from anyway.
It’s not really dangerous to handle as long as you know that it’s very cold. You can pick it up with bare skin no problem as long as you keep moving it around in your hand. A favourite party trick of my old lab supervisor was to pop a little lump of it in his mouth and snort great dragon-like clouds of steam out of his nostrils. Needless to say I also did this on several occasions and never injured myself - you just need to keep it moving around your mouth and not let it sit in one spot.
I used plenty of it this morning. But you probably wouldn’t want it though, as it’s not food grade.
The other problem with stocking dry ice is that it will sublimate on you eventually, no matter how you’re keeping it. So it doesn’t surprise me that not many places would keep it around.
When I was in college, we had a little device that made about 1 kilo blocks of dry ice by forcing compressed CO2 through a membrane and letting thermodynamics do all the work. Worked pretty well, but I don’t think you’d want to spend whatever it cost for that, even though getting a CO2 tank shouldn’t be that hard.
a person in a lab likely would have considerable experience in handling dry ice.
an inexperienced person could easily suffer frostbite in handling it improperly. if it comes into contact with any moisture on your body it could freeze that moisture and be stuck to your body causing frostbite. lingering or tight contact even when dry can cause frostbite.
placing it in a closed container could result in that container exploding.