The Chow test is a test for parameter stability between time periods or different groups.
The Chow test is used to test for structural breaks over time or for differences between subgroups of a sample. Suppose you have a general linear model of the form $$y_i = \alpha + \beta X_i + \epsilon_i$$ and you want to test whether $\beta$ is the same for two groups, $A$ and $B$, i.e. $\beta_A = \beta_B$. For the following regression $$y = \alpha + \beta_1 X_i + \beta_2 (X_i\cdot D_A) + \beta_3 D_A + \epsilon_i $$ where $D_A = 1$ for units of group $A$ and zero otherwise, a Chow test is a simple F test on the coefficients $\beta_2$ and $\beta_3$. A rejection of this F test ($\beta_2 \neq 0$ and $\beta_3 \neq 0$) means that $\beta$ is not the same across the two groups. The coefficient $\beta_2$ gives the difference between the two groups $\beta_A - \beta_B$.
The group example easily extends to the time-series context where a structural break Chow test is performed by comparing the hypothesized pre- and post-break periods. For an example how to implement the Chow test in Stata and also with multiple groups is provided in a Stata FAQ article by William Gould.
