We have the same problem with an open chat only blinking on the taskbar. We have asked numerous times to have a check box that will allow a toast pop up or bring the chat to the front when a message is sent each time just like it does the first time you recieve the message but it has been rejected as an enhancement so far.
The only other option we have been given is to have UCA play a sound when a message is sent. You can access the sound that is played when UCA Chat Message is Recieved by going to the Windows Control Panel and clicking on Sound. In the Sound application, click on the Sounds tab. In the Program Events list, scroll down and find Unified Communicator Advanced Sounds and pick the sounds you want for the various options like "Chat Message is Received".
It seem like Mitel thinks chat is not something you should start with someone and then open another app or work on something else that covers it up. I, like you, just wish it had better options for notifications of incoming chats so I didn't have to hear from my frustrared users all the time. For what it is worth, they have told me it is patterned after Microsoft Instant Messanger, which I guess hast he same behavior.