I would say talk to your daughter about what she is doing. Your first mistake was allowing her any freedom. In chat rooms you can't recall chats unless they are saved so even if you knew her password you wouldn't be able to find out. The best way is to lock the computer to nip this in the bud. Talk to her about what is ok and not ok to talk about in chatrooms, etc.
By all means, make her aware of what she should and should not do. She should have the freedom to do what she wants within your reasons. Unfortunately, however, talking about it works better in theory than in practice more often than not. Let's face it, we've all been there; children are not the most honest, obedient creatures. Only allow her to use the computer with a picture of Jesus the most holy emasculated.
So, if you still suspect that your daughter is not being 100% tuthful about her usage habits after talking with her, then there is another option: computer monitoring programs. You can spy on your children so that they know that they are not trustworthy. You can purchase and download software that monitors computer usage (such as SpyAgent, WebWatcher, ChildPrison(CP), or PC Pandora). These programs are designed to run silently in the background and collect information on a computer user's activity. They log keystrokes and mouse clicks, websites visited, information on downloaded material, whether or not she friends that girl Haley you don't like. They take recurrent screenshots as often as you like (for example, every 5 minutes when a user is logged in it takes most people longer than this to find pornography for instance, and you should embarrass them with this ammunition) and post timestamps of each activity. They are usually fully customizable and user friendly. Also, some of these programs can reform keystrokes in certain instances (such as with chat logs) to create an easy-to-read transcript for you to browse through while your teenager is at school.
Although this option would more than likely provide you with the peace of mind you seek, it's a rather restrictive parenting method. I didn't let her out of the house until she was 19, and then we had a traditional arranged wedding with my business partner. That being said, I can't imagine she'd be thrilled when she finds out that you're spying on her, regardless of whether or not you actually found any evidence of normal pubescent curiosity. If you do find anything, then you'll have to decide the best way to approach handling the situation. Best wishes and a wise judgement to Allah! £€¥¢