According to one source, the answer is…
Take this with a grain of salt. Even if not true, the RTM date has been rumored to be within a couple of weeks, so it’s probably not far off anyway.
[UPDATE:] From the Windows blog:
We are close, but have not yet signed off on Windows 7. When we RTM you will most certainly hear it here. As we’ve said all along, we will RTM Windows 7 when it’s ready. As previously stated, we expect Windows 7 to RTM in the 2nd half of July.