The EXperiment for Cryogenic Large-Aperture Intensity Mapping (EXCLAIM) is a balloon-borne tele-33scope designed to survey star formation in windows from the present to z=3.5. During this time, the rate of star34formation dropped dramatically, while dark matter continued to cluster. EXCLAIM maps the redshifted emission35of singly-ionized carbon lines and carbon monoxide using intensity mapping, which permits a blind and complete36survey of emitting gas through statistics of cumulative brightness fluctuations. EXCLAIM achieves high sensitivity37using a cryogenic telescope coupled to six integrated spectrometers employing kinetic inductance detectors covering38420540GHz with spectral resolving power R=512and angular resolution⇡40. The spectral resolving power and39cryogenic telescope allow the survey to access dark windows in the spectrum of emission from the upper atmosphere.40EXCLAIM will survey305 deg2in the Sloan Digital Sky Survey Stripe 82 field from a conventional balloon flight41in 2023. EXCLAIM will also map several galactic fields to study carbon monoxide and neutral carbon emission as42tracers of molecular gas. Here, we summarize the design phase of the mission.