Let's analyze the problem step by step:
- The circle has center at the origin and radius 1.
- Points $X, Y$, and $Z$ lie on the circle such that the length of arc $\(X Y Z\)$ is $\(\frac{2}{3} \pi\)$.
- We need to find the length of chord $X Z$.

Interpretation:
The arc $X Y Z$ is the arc from $X$ to $Z$ passing through $Y$. The arc length is $\(\frac{2}{3} \pi\)$. Since the radius is 1 , the arc length is equal to the central angle (in radians) subtended by the arc. Therefore, the central angle $\(\theta\)$ for arc $X Y Z$ is $\(\frac{2}{3} \pi\)$ radians.

However, note that the chord $X Z$ subtends the same central angle as the arc $X Y Z$, which is $\(\frac{2}{3} \pi\)$ radians. So, the chord length from $X$ to $Z$ can be found using the chord length formula for a circle of radius $r$ and central angle $\(\theta\)$ :

$$
\(\text { Chord length }=2 r \sin \left(\frac{\theta}{2}\right)\)
$$


Here, $r=1$ and $\(\theta=\frac{2}{3} \pi\)$ :

$$
\(\text { Chord length }=2 \cdot 1 \cdot \sin \left(\frac{\frac{2}{3} \pi}{2}\right)=2 \sin \left(\frac{\pi}{3}\right)\)
$$

We know that $\(\sin \left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2}\)$, so:

$$
\(\text { Chord length }=2 \cdot \frac{\sqrt{3}}{2}=\sqrt{3}\)
$$


Therefore, the length of chord $X Z$ is $\(\sqrt{3}\)$.
Answer:

$$
\(\sqrt{3}\)
$$


This corresponds to option (B).