The most cost-effective solution will be to roll your own using AWS services.
AWS AppSync can get you started by launching a CloudFormation template to provision the services you need for your backend.
You'd have to take care of UI yourself but there are plently of Chat UIs for various web-frameworks.
Another idea is to setup your own MQTT server. I had some experience using this for building a chat app that was launch into the india market and needed to work at scale.
Thank you Andrew
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