Even though it evaluates the upper tail area, the chi-square test is regarded as a two-tailed test (non-directional), since it is basically just asking if the frequencies differ.

Is chi squared always right tailed?

Chi-square tests are always right-tailed tests. If p ≤ α reject the null hypothesis.

How do you know if a test is one tailed or two-tailed?

A one-tailed test has the entire 5% of the alpha level in one tail (in either the left, or the right tail). A two-tailed test splits your alpha level in half (as in the image to the left).