Single-and few-layer chromium triiodide (CrI3),which has been intensively investigated as a promising platform for two-dimensional magnetism,is usually prepared by the mechanical exfoliation.Here,we report direct growth of single-layer CrI3 using molecular beam epitaxy in ultrahigh vacuum.Scanning tunneling microscopy (STM),together with density functional theory (DFT) calculation,revealed that the iodine trimers,each of which consists of three Ⅰ atoms surrounding a three-fold Cr honeycomb center,are the basic units of the topmost Ⅰ layer.Different superstructures of single-layer CrI3 with periodicity around 2-4 nm were obtained on Au(111),while only the 1 × 1 structure was observed on the graphite substrate.At an elevated temperature of 423 K,single-layer CrI3 began to decompose and transformed into single-layer chromium diiodide.Our bias-dependent STM images suggest that the unoccupied and occupied states are spatial-separately distributed,consistent with the results of our DFT calculation.We also discussed the role of charge distribution in the super-exchange interactions among Cr atoms in single-layer CrI3.