This work describes the optical design of the EXperiment for Cryogenic Large-Aperture Intensity Mapping(EXCLAIM). EXCLAIM is a balloon-borne telescope that will measure integrated line emission from carbonmonoxide (CO) at redshiftsz <1 and ionized carbon ([CII]) at redshiftsz= 2.5−3.5 to probe star forma-tion over cosmic time in cross-correlation with galaxy redshift surveys. The EXCLAIM instrument will observeat frequencies of 420–540 GHz using six microfabricated silicon integrated spectrometers with spectral resolv-ing powerR= 512 coupled to kinetic inductance detectors (KIDs). A completely cryogenic telescope cooledto a temperature below 5 K provides low-background observations between narrow atmospheric lines in thestratosphere. Off-axis reflective optics use a 90-cm primary mirror to provide 4.2′full-width at half-maximum(FWHM) resolution at the center of the EXCLAIM band over a field of view of 22.5′. Illumination of the 1.7 Kcold stop combined with blackened baffling at multiple places in the optical system ensures low (<−40 dB) edgeillumination of the primary to minimize spill onto warmer elements at the top of the dewar.