There's a lot of controversy but very little hard-core research on the topic. We do know that very few granite slabs “outgas” levels of radon high enough to register on lab equipment. And even with those, room size, amount of ventilation and other factors may prevent any buildup to levels the EPA considers a health hazard. But if you want to test your counters, purchase a do-it-yourself test kit (available online or at some home centers).
Follow the kit instructions for test packet placement. Leave the packets in place for the recommended amount of time and record all requested room sizes on the return envelopes. Then mail them in for analysis. If the results show a higher concentration of radon in the kitchen, contact a local testing laboratory for a more thorough analysis before you start ripping out your new countertops.
Radon gas can pose a serious health threat. But you should keep the issue of radon and granite countertops in perspective. Radon is far likelier to enter your home through cracks in your basement slab or foundation. If you're concerned about the possibility of radon in your countertops, test them. But check your basement or lower level first.