(-2)*loglikelihood ~ Chi-square? I just vaguely remember that I have learned something like "(-2)*loglikelihood asymptotically follows Chi-square distribution." However, I failed to find the relevant theorems in the textbook. Does anyone know the right theorem for this? Many thanks!!

It is called Wilks' theorem. It says that minus twice the logarithm of a maximum likelihood ratio statistic asymptotically approaches the chi-squared distribution as the sample size approaches infinity. Take a look at this.