We present a near-IR survey for the visual multiples in the Orion molecular clouds region at separations between 100 and 1000 AU. These data were acquired at 1.6~$mu$m with the NICMOS and WFC3 cameras on the Hubble Space Telescope. Additional photometry was obtained for some of the sources at 2.05~$mu$m with NICMOS and in the $L$-band with NSFCAM2 on the IRTF. Towards 129 protostars and 197 pre-main sequence stars with disks observed with WFC3, we detect 21 and 28 candidate companions between the projected separations of 100---1000 AU, of which less than 5 and 8, respectively, are chance line of sight coincidences. The resulting companion fraction ($CF$) after the correction for the line of sight contamination is 14.4$^{+1.1}_{-1.3}$% for protostars and 12.5$^{+1.2}_{-0.8}$% for the pre-main sequence stars. These values are similar to those found for main sequence stars, suggesting that there is little variation in the $CF$ with evolution, although several observational biases may mask a decrease in the $CF$ from protostars to the main sequence stars. After segregating the sample into two populations based on the surrounding surface density of YSOs, we find that the $CF$ in the high stellar density regions ($Sigma_{YSO} > 45$~pc$^{-2}$) is approximately 50% higher than that found in the low stellar density regions ($Sigma_{YSO} < 45$~pc$^{-2}$). We interpret this as evidence for the elevated formation of companions at 100 to 1000 AU in the denser environments of Orion. We discuss possible reasons for this elevated formation.
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