Tellurite glasses are important as a host of Er3+ ions because of their good solubility and because they present broadband optical gain compared with Er3+-doped silica, with the potential to increase the bandwidth of communication systems. However, the small glass stability range (GSR) of tellurite glasses compromises the quality of the optical fibers. We show that the addition of CsCl to tellurite glasses can increase their GSR, making it easier to draw good-quality optical fibers. CsCl acts like a network modifier in glass systems, weakening the network by forming Te-Cl bonds. We show that the thermal expansion coefficient mismatch is in the right direction for optical fiber fabrication purposes and that the Bi2O3 content can be used to control the refractive index of clad and core glasses. Single-mode and multi-mode Er3+-doped optical fibers were produced by the rod-in-tube method using highly homogeneous TeO2-ZnO-Li2O-Bi2O3-CsCl glasses.