Chi-sqaured values vs sigma and mean uncertainties

I have a very simple question, but I do not know the answer, so perhaps someone can help me:

When I fit a Gaussian to my histograms I get very low errors on both my mean and sigma (on the order of a tenth of a percent) yet my reduced chi-squared is often 2 or 3. I am not sure why this is the case. Shouldn’t my uncertainty in sigma and the mean be higher if my chi-squared is that high?

What exactly is ROOT doing?

Any help would more than appreciated.

Thanks in advance,