Yes, you need one. avast is not a suite (antivirus + firewall).
Personal Firewall Tests & Results. Firewall rating:
http://www.matousec.com/projects/windows-personal-firewall-analysis/leak-tests-results.php#firewalls-ratings

Freeware firewalls:
http://www.firewallleaktester.com/tests_overview.php
http://www.thefreecountry.com/security/firewalls.shtml
http://forum.avast.com/index.php?topic=22742.0;topicseen