Any applicant appealing the rejection of a claim (termed an appellant) may request an oral hearing before the Board of Patent Appeals and Interferences. The oral hearing request must be filed not later than 2 months after the mailing date of the Examiner's answer. This response period is one of the few that may not be extended by petition and payment of a fee under 37 CFR 136(a).
The position of the USPTO on this issue is described in the following section(s) of the Manual of Patent Examining Procedure (MPEP):
MPEP 1209 - Oral Hearing
Law - Oral Hearing Request