We have investigated the chiral charge-density wave (CDW) in $1T$-VSe$_2$ using scanning tunneling microscopy (STM) measurements and optical polarimetry measurements. With the STM mesurements, we revealed that the CDW intensities along each triple-$q$ directions are different. Thus the rotational symmetry of $1T$-VSe$_2$ is lower than that in typical two-dimentional triple-$q$ CDWs. We found that the CDW peaks form a kagome lattice rather than a triangular lattice. The Friedel oscillations have the chirality and the periodicity reflected properties of the background CDW. With the optical measurements in $1T$-VSe$_2$, we also observed a lower rotational symmetry with the polarization dependence of the transient reflectivity variation, which is consistent with the STM result on a microscopic scale. Both $1T$-TiSe$_2$ and $1T$-VSe$_2$ show chiral CDWs, which implies that such waves are usual for CDWs with the condition $H_mathrm{CDW} equiv q_{1}cdot(q_{2} times q_{3}) eq0$.
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