Goodness of fit for multivariate gaussian

What are good tests to check if the data is generated by multivariate jointly gaussian distribution.

I know $\chi^2$ test is commonly used as a goodness of fit metric but I did not understand how to use it for multidimensional random vector case. Most of the examples I saw were for univariate cases.

An example would help a lot.

Note: the covariance matrix isn't diagonal. No assumption of independent variables.