According the general rule, the party noticing the deposition of a treating doctor must pay for his time. The general rule is stated in Illinois Supreme Court Rule 204(c)--
Depositions of Physicians. The discovery depositions of nonparty physicians being deposed in their professional capacity may be taken only with the agreement of the parties and the subsequent consent of the deponent or under a subpoena issued upon order of court. A party shall pay a reasonable fee to a physician for the time he or she will spend testifying at any such deposition. Unless the physician was retained by a party for the purpose of rendering an opinion at trial, or unless otherwise ordered by the court, the fee shall be paid by the party at whose instance the deposition is taken.
Rule 204(c). The last sentence contains an exception to the general rule: it does not apply when "the physician was retained by a party for the purpose of rendering an opinion at trial." When the doctor-deponent is a retained expert, it doesn't matter which side scheduled the deposition: the retaining party must pay the deposition expense. Id.; see also Vicencio v. Lincoln-Way Builders, Inc., 204 Ill. 2d 295 (2003).
What about a cases in which a treating doctor is also going to render an opinion? According to Vicencio, the general rules applies: the party noticing the deposition must pay the fee. Id ("a nonparty treating physician, even though he or she may offer an opinion during testimony, is not an expert or opinion witness in the sense used here").
Vicencio also contains a discussion about what deposition expenses are taxable as costs.