Click 'Start'.
Type 'def' into the box.
Click on 'Default programs'
Click on 'Associate a file type or protocol with a program'
Scroll down to the entries for '.htm' and '.html'.
That will show you what Windows will try to open web pages with. You can change an entry via double-clicking on it and then selecting the program of your choice.
If Internet Explorer is shown, try changing both entries to Chrome. If Chrome is shown but you're happy enough for links to open in Internet Explorer, try changing them to IE. If Chrome is shown and you'd really like to use Chrome to open links, try changing them to IE, restarting your computer and then changing them back to Chrome again.
If none of that works, check the registry entry referred to in Archer's post here:
http://www.sevenforums.com/microsoft-office/317028-outlook-2010-wont-open-hyperlinks-chrome-win-7-home-premium-64-a.html
(PS: As a short term fix, you might be able to copy a link from a 'button' via
right-clicking on it but, as it's a long time since I've used Outlook, I can't be sure).