Java currently has an unfixed glaring exploit, so apple has disabled all versions of java 6 and java 7 from running on any mac just today.
Given the timing of the question, I'm assuming you're running a mac. Correct me if I'm wrong.
In regards if it's safe to run java, well, java does introduce security holes into computers, so I wouldn't say it's completely safe. But if you keep it updated, run security software, and ideally have a backup of your harddrive, you can really make the risk minimal. IMO, a minimal risk of java exploits is worth going on all of chess.com.
Ok, this site is my main baby, but I really enjoy using another site for improving my chess and and in that area I think it has help more then the learning tools here except for the videos. But I am having trouble with java which is needed to enter the training room, and the plugins will not work all of a sudden. I guess changes came about because some browsers are dropping java because it seems to be a port hole for mal wear and can damage your computer. So I am uncertain if I should restablish java and use it, or stay away from java? Any opinions would greatly help me! decide!