Flip the chair over. If you can see any intersecting metal pieces you can oil them at the intersections. What has happened is the springs have rusted a little and now they make noise when they rub together. However, oil is a short term solution. You need to put a thing but strong piece of nylong in between the springs where they rub together. Try using teflon tape found in the plumbing department.
If there is material in the way, you will have to remove the staples/nails/brads to remove the material and get at the springs.
Add your voice to the conversation. Click here to answer this question.