No.  They are not required to test your water.  However, there is huge incentive to test any water well within a 1,000 feet of their gas well.  In that zone, the gas company is “Presumed Responsible”  (i.e.,  guilty until proven innocent) for drinking water contamination unless they have conducted a pre-drill test that clears them.  Testing a well outside of 1,000 feet would be at their discretion.

• Test for particular contaminants (their test might not cover contaminants you should test for)
• Test your water after drilling (there is NO INCENTIVE after they finish drilling)

Conflict: if the gas company tests your water, they're better off if your water is dirty

Consider a water test with a split sample.  Your independent representative takes a sample at the same time as the gas drilling company, verifying the accuracy of their test results.

[Cabot] does not want to release the 2008 water tests because they contain private information about landowners -- Cabot spokesman George Stark, September 16, 2010