Chirality is an important concept in particle physics and the condensed matter field in relation to baryogenesis [1] or spontaneous symmetry breaking. In condensed matter physics, many researchers have attempted to study the chiral properties of $^{3}$He-A [2] and chiral p - wave superconductors [3, 4]. Is it possible to break the chiral symmetry in electron systems that also have macroscopic quantum order such as charge density waves (CDWs)? 

Chirality is often characterized by using the parameter of helicity h = σ · p / | p | ( σ :spin p :momentum) in a photon, or h = v · ω ( v :velocity, ω :vorticity) in fluids. If the helicity is nonzero in a system, the system has chirality. Chirality describes the character of an object or structure that cannot be superimposed on its mirror image. So far, there is no evidence of the chirality in one-dimensional (1D) CDWs and two-dimensional (2D) CDWs, as usual, since a CDW has the form ρ =cos( kx + φ ) ( ρ : charge density, k : wavenumber, x : position, and φ : phase), which is invariant by space inversion, or parity transformation ( k → ( − k ) and x → ( − x )). 

In this paper we report the chirality of a CDW in 1T-TiSe$_{2}$ [5–12] measured directly by using STM and optical ellipsometry. STM is used to investigate the microscopic electron distribution and the phase of the CDW order parameter in real space [5, 6, 13]. In the measurement, the CDW intensity becomes Ia$_{1}$ : Ia$_{2}$ : Ia$_{3}$ = 1 : 0 . 7 ± 0 . 1 : 0 . 5 ± 0 . 1, where Ia$_{i}$ (i =1, 2, 3) is the amplitude of the tunnelling current contributed by the CDWs. We then found two states with different helicities. When we index each nesting vector in order of intensity in the Fourier transformation of the STM images, the three intensity peaks of the CDW decrease clockwise and anticlockwise . Moreover, the two-color pump-probe pulse method was performed to determine the macroscopic property of the relaxation of excited electrons by pump laser pulse. The direction dependence in transient reflectivity has two- fold symmetry. Since it is impossible to explain the electron distribution using conventional CDW theory as with 1T-TaS$_{2}$, we propose a new CDWs configuration based on the three- dimensional (3D) nesting vectors of 1T-TiSe$_{2}$ in reciprocal space. In real space, a phase shift along the nesting directions can reduce the Coulomb interaction and the phase shift between three nesting vectors induces helical stacking in CDW unit cell. As a result, the CDW system has chirality based on the direction of helical stacking. 

We provide the first evidence of chirality in a CDW. Moreover, we propose generalized CDW chirality in a triple- q system, 

1T-TiSe$_{2}$ crystallizes in a 1T-CdI$_{2}$ type structure. The crystal is constructed of Se-Ti-Se 

