Hi,
There are a few issues at play here, so I'll do my best to explain them in order.
If you bought the chairs with both you (as the customer), and the retailer being that you are buying them "as a pair", then the retailer could well have to agree to refund or replace both chairs. But ONLY if they sold them to you "as a pair".
If, however, you just bought two, because you needed two chairs, then the retailer is only liable to refund, repair or replace the faulty item.
As such, you may have to either:
1) If they will let you, give them back both chairs you currently own, and look for another pair from the same place, for a similar price.
2) Or, simply accept the fact that you will have one chair that will have to be kept by you, or sold on via classified ads, in order for you to go away and buy a new pair of chairs instead.
Personally, I think your options are likely to be:
1) Store will llet you return both, as long as you replace them with another pair to your liking, from them (with items of a similar or higher cash value), or
2) You return just the faulty chair, and end-up having an odd chair in your house!
You may well, have to accept to take this case "on the chin", as the retailer has no legal requirement to refund you for both chairs, unless they knowingly sold them to you on the basis that you were looking for a pair of identical chairs.

Sorry.
Pooch