How can I clean an office chair?
In all probability, you're probably smelling volatile organic compounds in the glue and other chemicals used in the process of making the chair.

If this is your problem, there's not much you can do, other than to air the chair out completely.

Can you set it outside for a day or two (protected from the elements and pilferage)?

If outside isn't an option, set it near an open window and point a box fan or similar at it for a couple of days.