Should I buy this is it possible to repair (Finn Juhl).  

yes
if its not too expensive, any wood furnture can be repaired if you care enough and find the right person to do it. Is the crack on the backrest stretcher or the t section? Bigger photos would be good.
Any exposed end grain next to straight grain often looks different.
Beautiful chair!

Thanks for your help so far.
The chair is Bovirke ,and the crack is on the T section.Would $1300 be too high for this?I really like the chair ,and it is the first one I've seen in my price range.

maybe 🙂
ask them to...
maybe 🙂
ask them to knock 25 % off

This
crack looks a lot like a saw cut. It would not respond to a simple glue repair, from what I can see. Another photo would be helpful.

Thank you all for your advice.
Thank you all for your advice.I think I am going to steer clear of this chair.I know the seller is going to be very disappointed though.It really is a shame though I've always wanted one of these chairs.

Probably a
good idea. On further inspection, however, I believe this is a crack rather than a cut. It may be glueable -- for what it's worth. I'm still trying to identify the location. Maybe the photo is upside down ?

Where is the break exactly?
Where is the break exactly?

I am a five hour drive from the chair.
Unfortunately I am actually not in the same city as the chair ,and all I have is two photos similar too this.All I was told by the seller exact words was that the crack was on the backside of the top arm joint (what ever that means).Anyways the chair was also a super cheap deal ,but I guess a number of us addicts bid each other way up on it.I was the top offer at $1100 plus $200 for gas to drive it to me.I really want the chair bad ,but I don't want to make a big mistake.I really am not looking forward to calling the seller to cancel.I will post the larger photo of the damage I have in my email shortly.I sure someone who was offering against me will probably notice this.Makes me sad.

larger pic.
This one is larger.

not good
Judging from that picture alone...truly is questionable. The location, as if you were sitting in the chair, would be on the arm rest, near where the elbow would sit. A delicate location...damage in that area can be well repaired, but high potential of re-breaking. Too much weight pushing down could cause a snap...even cause events towards bodily harm.
Minty Bovirke models I've seen.. more or less...sold in the $1500-$2500 range. My incomplete opinion....the damage on that chair would bring the price to under $1000 USD.
These chairs have been produced in a sufficient quantity, that you'll be able to acquire one at a reasonable price...IMHO

BTW
That repair is such a shoddy job...

I don't think
there's been a repair, yet. Which is a good thing. I assume there's a dowel or tenon at this joint, and it must have been cracked or moved in order for the visible break to have occurred. These are my guesses. Perhaps the joint could be disassembled completely and reworked. No wood is missing, apparently. I doubt that it would be enough just to glue the visible break, which occurred where the grain of that upper part is short because of the curved ("bent" shape of the piece.
I would probably proceed by making a clean cut at the joint, gluing the visible break, and drilling both halves of the joint for a new dowel.
If the chair is a real bargain, and you have access to an expert woodworker, you might consider purchasing the chair.

I wouldn't take my chances wi...
I wouldn't take my chances with this chair. Instead I would save up another $300-$500 additional to the approx. $1400 you're expecting to spend buying, delivering and reparing this chair. Then you can get one that's completely ok and will hopefully last your lifetime.
The FJ45 chairs made by the original maker, Niels Vodder, is going through the roof here in Denmark. A few monts ago a pair in a very beautiful palisander sold for $27.000 + auction fees.