Looks like India, 2nd half of the 20th century, not worth much because ivory regulations have become more strict.
Ever seen this chess set?
It seems to be either ivory or faux ivory from your picture and it would be pretty surprising if this kind of set were faux ivory.
If you zoom your picture up it's pretty clear, on (ironically, the elephant), next to the royal pieces... you can see schreger lines running vertically down the piece. I don't really see them cross each other, so I won't discount the possibility this could be something like plastic made in layers to fake them, or really I suppose even bone with schreger lines painted on to it is possible even if they did cross, but I think it would be very weird if someone faked this kind of set, so I feel reasonably sure it's ivory. Nothing wrong with asking a specialist either.
From your picture the box doesn't look different from the typical tourist sets, Rajasthan, Maharajah style which we know are much later than that but there could be something telling about the box that doesn't show in your picture. This is hard because there used to be better community resources for talking about antique chess sets through eBay groups and they're pretty much closed down. Your set is not any of the typical ones which are easy to find in several places online but I have the feeling I've seen it before and I yet I can't find those resources anymore.

From your picture the box doesn't look different from the typical tourist sets, Rajasthan, Maharajah style which we know are much later than that but there could be something telling about the box that doesn't show in your picture. This is hard because there used to be better community resources for talking about antique chess sets through eBay groups and they're pretty much closed down. Your set is not any of the typical ones which are easy to find in several places online but I have the feeling I've seen it before and I yet I can't find those resources anymore.
I have quite a lot of vintage chess set and I have the impression that this box is not from 20th century. The guy I asked his a professional seller with a huge experience, and I tend to accept his opinion, although I only can be sure after showing him the set instead of a picture. He said immediately that the box is typical from the early 19th.
Anyway, I never saw a similar set in internet or literature.
Ok, it's pretty hard to believe you've seen a lot of vintage chess sets and not one that similar to this before. In my experience antique dealers don't tend to know chess sets well if they're not one of the few "chess set dealers," who do still exist, ... ok it looks like Garrick Coleman passed away, Tim Millard, Frank Camaratta, even someone like Marco Dorland, etc... you could still ask, even some others who are simply collectors have compiled the resources that were once online, scans of every chess auction for many years (although you can't trust those, often the auction house is not expert) I think these pages are Jon Crumiller's? http://chessreference.com/Catalogs/ I haven't looked through all of the catalogs here by you may find your set there. Asking Alan Dewey is something else I might do but he worked on a lot of my sets back in the day, if you don't have a relationship with him and aren't asking for work done I'm not sure it wouldn't bother him to have random people asking for free opinions. Maybe it would be fine, could also be worth a shot.

I contacted once Crummiler, asking about another set and a rare Swiss chess clock. I didn't dare to ask him more questions. Perhaps I should try. Thanks.

Ok, it's pretty hard to believe you've seen a lot of vintage chess sets and not one that similar to this before. In my experience antique dealers don't tend to know chess sets well if they're not one of the few "chess set dealers," who do still exist, ... ok it looks like Garrick Coleman passed away, Tim Millard, Frank Camaratta, even someone like Marco Dorland, etc... you could still ask, even some others who are simply collectors have compiled the resources that were once online, scans of every chess auction for many years (although you can't trust those, often the auction house is not expert) I think these pages are Jon Crumiller's? http://chessreference.com/Catalogs/ I haven't looked through all of the catalogs here by you may find your set there. Asking Alan Dewey is something else I might do but he worked on a lot of my sets back in the day, if you don't have a relationship with him and aren't asking for work done I'm not sure it wouldn't bother him to have random people asking for free opinions. Maybe it would be fine, could also be worth a shot.
I even don't know how many sets I have. I have a lot of regence, Stautons, Vienna cafe house, travel sets, compendium, clocks, Biedermeier, and so on.

Most of my items I bought in flea markets for few money. My both Solora clocks for example I pllayed only something like 10 or 15 dollars each.
Well, that's impressive (your good finds I mean). Re contacting Jon Crumiller, IME he has been very personable and kind to collectors with questions but it's been many years and random people from the internet may not be the same as collectors in a community group specifically for chess which he was also member of at the time. Good luck.
I purchased this amazing chess set in an antiques market in Switzerland yesterday. I didn't find any similar set in my books or in the internet. Perhaps you saw it already somewhere? I am interested in any information: age, origin, price.
Thanks