Basically, sampling distributions are derived assuming the null hypothesis is true. There will also be an expected value (mean) and a standard error associated with the sampling distribution. As such, the sample statistics (under the null) will vary due to random chance factors alone....They can be small e.g chi-square = 0 or large chi-square = 18.5 (just to throw a number out).
To use your example, the mean of a sampling distribution of a chi-square statistic with df=3 (assuming the null is true) will be 3 (not zero). Note that zero is a lower limit.