What a great news! TLS/SSL is finally supported in the chrome.sockets API in the last chromium build. This means secure connections¹ over the network between your Chrome App and servers.
I'm sure we're going to see this brand new chrome.socket.secure method being used in many Chrome Apps like CIRC² and Advanced REST client³.
² https://github.com/flackr/circ ³ https://github.com/jarrodek/advanced-rest-client