We did some internal testing with HCL and IE and Firefox, and the chat connections seemed to go through normally. Are you using a recent version of Firefox? If you search these forums, there is a patch that's supposed to fix a problem with early versions of Firefox 3. I haven't seen the problem myself, and so never applied it. Otherwise, yes, I believe there are known issues with other browsers including Safari and Chrome. Unless you're a good PHP programmer, the solution is to wait for HCL 3.0.
We found the current user <-> operator transport to be buggy in a number of other ways, too. In the meantime, you might try Livezilla or Crafty Syntax, which are also both free.
BTW, you posted in the HclApp forum, which isn't really for general questions,. I believe HclApp is a Windows HTML application (.hta) for HCL configuration or use....never tried it myself.