proof of a property of the Chi-Squared distribution

Hi

I was wondering if someone could please provide me with the proof of the following property of a Chi-Squared distribution.

If $\displaystyle X_{1},X_{2},..........,X_{n}$are random observations from a normal distribution with parameters$\displaystyle \mu$ and $\displaystyle \sigma$, then the statistic

$\displaystyle \frac{1}{\sigma^{2}}\sum_{i=1}^{n}(X_{i}-\overline{X})^{2}\approx\chi_{n-1}^{2} $where$\displaystyle \overline{X}=\frac{1}{n}\sum_{i=1}^{n}X_{i}$is the sample mean

Thanks