Thonet?  

here's the pic (I hope)
here's the pic (I hope)

Contact the Thonet museum
I would email the Thonet museum. If you attach a pic they should be able to help you.

Did you
look underneath on the inside of the seat rim for the Thonet logo burned into the wood? Or evidence of an old rectangular paper label? If you don't see either one or the other, I would be hesitant to say it was Thonet.
Although, I must say, it is a beautiful chair and I would love to own it even if it isn't Thonet. The patina of the wood is fabulous.

Thanks Riki! I checked...
Thanks Riki!
I checked with my parents and there is indeed a Thonet label on the underside. I didn't have the chance to check myself, since the chair is at their place.
Any thoughts about the age?

If you go on
the Thonet website, they show you what the labels looked like all through the years. I have been able to date my Thonet chairs within a 10 year period using their website.

Here is a good
resource, but it is in "Franglish". If you need help translating, let me know.
http://www.aubonusage.com/signaturesetiquette/index-en.html

label
I couldn't find the labels on their site, but based on the link you posted I'd say the chair is from the 1888-1922 period.
Looking at the quality woven seating (in between the
two examples on the site) I'd say it's from in between 1900 and the First World War.
Correct me if I'm wrong here 🙂
@Riki: could you point me to the labels on the official site?
Again, thanks for the info!!!
Here's a pic of the label, btw:

Here is your
chair, designed by Michael Thonet in 1895. Thonet #233.
http://www.thonet.de/en/233

Found that one already, but...
Found that one already, but it doesn't have the engraved border on the back piece. That's what puzzled me in the first place (before I knew it had a label). In fact, I still can't find one that has it.

Just got word back from Thonet...
They have a very nice customer service and informed me that it's Office Chair #3, produced in between 1881 and 1916.
Friendly people, over at Thonet!