A friend and I chat using AIM and AOL and she is constantly getting knocked offline. Her cable internet service is provided by AT & T. Is it possible that she's being disconnected by a call waiting signal? I know those things happenned with dial up but can it happen with cable too? She is using a PC. Is there a way to stop that call waiting signal during a chat like there was using dial up?

You say she has "cable internet" from AT&T. Do you mean DSL? If she is using DSL then there should not be a problem with call waiting.

AT&T customer service can tell you what the code that needs to be dialed in to suspend/pause call waiting (as a test).

It could also just be an unreliable internet connection. Is she having any other connectivity issues?

She should swap out the patch cable between the Modem and the next device in line. And check any and all patch cables for connectivity reliability. Just unplug each cable and plug it back in, tug lightly to make sure the connection is secure.

Another thing to try would be to power off everything then restart in the following order.

Modem - wait for all lights to normalize
Router - wait about 1 minute
Switch - (if used) wait about 1 minute
Computer - wait for complete boot up before doing anything
Make sure Windows has ALL of the current service packs and patches.
Fire up browser of choice and test for reliable connectivity
Then test chat to see if it is any better. May want to think of upgrading the chat client she uses.

Good luck

Could also be a background process with the computer. Something like antivirus/antihacker software that scans incoming/outgoing processes.

Drops from call waiting and the like were problems encountered with dialup modems. If this "cable internet" is ATT's Uverse, there should be no interaction of any sort.
Is your friend using a wireless link from PC to the ATT network interface device or router? Does she have service drops doing activities other than Chat?

Call waiting should not have any effect on your dsl signal. However non filtered phones or bad dsl filters do. 

Try unplugging all of your phones and see if the situation improves. Many home security systems are connected to the phone line as well.  Make sure you have a filter on every phone including your home security system. 

If you are still not getting a good steady dsl signal, the problem is most likely on AT&T's end and needs them to correct it.