It depends upon whether you're going to have your own chat server hosted or use a ready framework (like firebase etc), the UI part is not very costly nor the front end functionality but the whole technology in the background.

We created sever chat apps before, and the cost varied from 5 K to 20 K USD because of background tech. only.

This app cost calculator tool is also a good way to DIY, check out http://www.agicent.com/app-development-cost-calculator.

I am glad to consult you (I am a Pro app developer, consulting startups and entrepreneurs mostly).