Danish side chair ID?  

I believe that fabric tag is a clue that limits it to a few companies.  Now if only I could think which company(ies) I've seen stick that on their product....

Niels Eilersen is who I am thinking of that used fabric stickers like that:
http://www.lauritz.com/en/auction/illum-wikkelsoe-laenestol-af-teaktrae/...
I kind of don't think the chair is an N. Eilersen though, but I could be wrong....

Thank you, that was hugely helpful. When I looked for that I found a link to a perfect match for my chair on ebay to a marked example for Scantic Møbelværk.with the same cloth badge. Then I found this example on Lauritz for an armchair version: http://www.lauritz.com/en/auction/scantic-mbelvrk-armstol-palisander/i3560646/?param=showdesktopversion
So at least I know who made it, if not who designed it. Does Scantic company ring any bells?
And this seller on 1stdibs attributes it to Erik Christensen . Is this seller believable? https://www.1stdibs.com/furniture/seating/dining-room-chairs/set-of-four-rosewood-danish-modern-dining-chairs/id-f_910999/

Well since the seller would only go so far as an attribution, there is already doubt.  Why don't you ask the seller what the attribution is being made on.  If you are interested in buying them, the seller should certainly be interested in explaining why it says "Erik Christensen" on there.  
On the plus side, Erik Christensen does not really add anything to the value, so there is no financial incentive for it (unlike say attributing them to Arne Vodder, or Hans Wegner, or going all out and saying they are a Wegner & Juhl collaboration).
By the same token, I don't know where they would have come up with such an attribution.  I think Erik Christensen is the person who designed the boomerang chairs for Slagelse, which doesn't seem like an obvious connection.  Or perhaps it is a different Erik Christensen, as there must be thousands of them, with such a common name.  Perhaps Scantic was owned by one Erik Christensen.
Best thing to do would be ask that seller.
And I don't expect you will probably get past Scantic.  I would say you are doing exceptionally well even to have gotten that far.