How do I know if this chair is an antique?

It's hard to tell from a picture whether or not this chair is an antique. If there are any markings on the underside of the seat you might do some research to help you figure out if it is or isn't. You can look up manufacturers names and possibly find information that way. I copied this information for you:

Maker's Information

The underside of the chair often offers the best clues as to its general age. Look for a tag with manufacturing information, including a name, model number or even a year for chairs made in the last 80 years or so. If the tag features a website address, that's a huge clue that it is a modern reproduction. If there is no tag, look for a stamp or even handwritten information on the seat bottom, in case the chair was handmade. The Internet has information on many manufacturers and chair artisans, so you may be able to look this name up online.

Hardware

The way the chair is assembled is a big clue to its age. If modern phillips-head screws are on the chair, holding legs or the seat assembly in place, it's likely a modern chair. Slotted screws are somewhat older. Chair rails or the support assembly beneath the seat did not have screws at all on chairs made in the 18th century, whereas newer ones usually do, in the corner brackets. Some modern chairs made by artisans may not have screws either, but such chairs are likely marked with the maker's name somewhere beneath the seat.

Your chair is most unusual but I doubt it is 18th century. More likely 19th or even later. It appears to be maple. Hope you are able to definitively identify it, it is fun to know the history of such things.

Here are a few more pictures of the chair. I did not see any markings or stamps on it although there appears to be some sticker that is missing. I do not see any screws anywhere on the chair...

I would have it checked out by an antique shop or auction house.

Do not touch finish it is lovely.