installed skype today to make personal phone calls from computer to compter.

a check with www.grc.com indicates that one port is open, presumably a server port in the list

generated by zone alarm's firewall.

my question is: is this port required for the operation of skype and, if so, does this leave my computer open to hacking?

I would be vary wary of grc.com the guy is not as knowledgable as he pretends. do a search on google for grc to see other people opinions. Regarding skype, you can see what port it defaults to by clicking on tools -> options -> connection.