Is a software firewall needed with a router?

I had a usb modem and I recently got a Zyxel P660HW router,which has a firewall.I am a Zone Alarm user for a few years now,but I have been told that I dont need ZA now that I have a router.Is this true?Can I uninstall it or do I still need it?

To clarify a little bit, a hardware firewall will not protect you from any trojan or other malware that you might have on your comp when it tries to communicate to other computers on the internet without your authorization.. A software firewall will alert you when that happens

Having a host based firewall on your system is a good idea. Along with the perimeter firewall, you have implemented a "defense in depth" architecture that should provide you with enough protection. Most hostbased firewalls will do application monitoring so if you have a malware that's not on the approved applications list, the host-based firewall will alert you if that program tries to send data, in essence, host based firewalls have some simple HIPS functionality.