If you still want them to show up in your inbox, things get complicated. You would have to create filters to label every kind of message you do want notifications for, and then in the Gmail app you would turn off notifications for the inbox, followed by syncing and turning on notifications for the label you just created.
If you don't care if they show in your inbox, do the following from the web GMail:
- Go to
Mail Settings -> Filters -> Create new filter
email@example.com in the To field
Chat with in the Subject field
- Hit Next
Skip the inbox
- Hit Create Filter
Alternatively you could turn off the saving of chat history, which disables offline messages, but that has its own downsides.