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If you're in the US or Canada, you can send SMS from Google Voice. You can also switch to Hangouts and "continue receiving SMS messages as follow-me (i.e. if you're offline and receive a Hangout message, you'll get an SMS message)."
Google says that "by streamlining our services, we're able to focus on creating the best possible products for our users," but I suspect that Google wants to discontinue Gmail Chat and switch all the users to Hangouts.
Unfortunately, the SMS feature from Hangouts is more limited and supports less countries. When clicking this link, I get this message: "We're sorry, the feature you are looking for is currently only available in a limited number of countries."
There are plenty of other ways to send SMS online. You can use the SMS feature from Yahoo Mail or Yahoo Messsenger, use MightyText, which has a nice web app, browser extensions, an Android app and also integrates with Gmail.
{ Thanks, Beta Aly and Michael Hardt. }