We present a high-sensitivity spectral line survey of the high-mass star-forming region Orion KL in the 325-360 GHz frequency band. The survey was conducted at the Caltech Submillimeter Observatory on Mauna Kea, Hawaii. The sensitivity achieved is typically 0.1-0.5 K and is limited mostly by the sideband separation method utilized. We find 717 resolvable features consisting of 1004 lines, among which 60 are unidentified. The identified lines are due to 34 species and various isotopomers. Most of the unidentified lines are weak, and many of them most likely due to isotopomers or vibrationally or torsionally excited states of known species with unknown line frequencies, but a few reach the 2-5 K level. No new species have been identified, but we were able to strengthen evidence for the identification of ethanol in Orion and found the first nitrogen sulfide line in this source. The molecule dominating the integrated line emission is SO_2, which emits twice the intensity of CO, followed by SO, which is only slightly stronger than CO. In contrast, the largest number of lines is emitted from heavy organic rotors like HCOOCH_3, CH_3CH_2CN, and CH_3OCH_3, but their contribution to the total flux is unimportant. CH_3OH is also very prominent, both in the number of lines and in integrated flux. An interesting detail of this survey is the first detection of vibrationally excited HCN in the v_2 = 2 state, 2000 K above ground. Clearly this is a glimpse into the very inner part of the Orion hot core
