Susan's first and Beth's 1000th posts - how about that for one thread?
Susan, the exact screw you're looking for depends on the age of your chair (in the old days, it was a two piece unit; today it's a single piece), but you can probably find a substitute in a couple of ways.
First, it is similar to the following part numbers: 105236, 106918 and 110611 - these are screws used to assemble Aneboda and Hemnes beds, but would be of slightly different lengths. The one you need is 3 3/16" long - figure 6 cm. if you need metric meausrement, so if you can call another AU IKEA , they might be able to help you.
Or follow Beth's idea of taking another screw with you to a local hardware store. You might also want to take one of the barrel nuts with you (you'll find them in the 2 pieces that run between the two sides and hold the frame together) so you be sure you have the right thread size.
Just as an aside here, there are probably no more than a couple of dozen different hardware bits that are used in the assembly of 75% or more of the IKEA range (that sounds vaguely Yogi Berra-ish, but you know what I mean).
There are very few pieces that have unique bits that are specific to them, so that if you can find a piece that is similarly constructed, you can substitute the hardware from one into the other.
As an example, the same dowels, cam locks and screws that are used to assemble the
Akurum
cabinets are the exact same ones that you'd use to do a Billy bookcase, just in different numbers; the same cam locks and screws go into Malm dressers and drawers, also.