Here is ist of compatibe hosting providers. If you want to appear in this list there is 120$ yearly fee.
Really releable hosting and I know these guys personally. Also I have tested their hosting plans personally, they even give an ssh with their minimal hosting plan. You can be sure that LHC will work as expected and no nonsense with mod security or any other limitation. For just Live Helper Chat purposes I recommend to choose either Mini or Midi plans. The only difference is that.