New vacuum chambers have recently been installed in the interaction region of the Cornell electron-positron storage ring (CESR) in order to improve the pumping and reduce the operating pressure of the collider in the vicinity of the (CLEO) detector as the beam currents are increased by a large factor. Lost-particles generated by the beams interacting with the residual gas are a major source of background in CLEO and could lead to radiation damage of sensitive components such as the new silicon vertex detector electronics installed around a two-centimeter radius beryllium beampipe. This article shows how titanium-sublimation pumps are used as an inexpensive and efficient way to attain pressures in the low nanotorr range in the face of large outgassing induced by intense synchrotron radiation. Laboratory measurements of pumping speed in these chambers using calibrated leaks are compared against performance in the ring. A history of the dynamic pressure rise in the ring (Torr/mA) since the most recent start-up of CESR will also be shown.