Domain walls (DWs) have been recognized to play crucial roles in various interesting properties and functionalities in quantum materials. A notable example is DWs in charge density wave (CDW), which are believed to provide metallic electron channels for emerging superconductivity. However, electronic states of DWs and the microscopic mechanism toward superconductivity have been elusive. Here, we clarify the atomic/electronic structure of DWs of the chiral CDW emerging in 1T-TiSe2, using scanning tunneling microscopy and density functional calculations. We reveal unambiguously the microscopic origin of chiral CDW as the C2 distortion in Se layers and its interlayer coupling. We further identify unique DWs connecting CDW domains of opposite chirality. The DWs are endowed with no in-gap state due to the characteristic multibands around the band gap, which defies the widely believed notion for CDW DWs. These results provide an important insight into the role of DWs in emerging superconductivity.