Bick
I'm using Firefox and I don't even see the 'hyperlink chain' icon.
Check your user settings. Go to your user info box to the right of the page and click on "Community settings". On the page that opens, click on the "Advanced settings" tab and under "Site Options", make sure that your "Content Editor" drop-down has "Enhanced" selected, not "plain text".
Also note that the link (chain) icon is usually greyed out until you have a word or block of text selected.