OS X Mavericks Push Notifications in Chrome

No, as it's specifically Safari Push Notifications using Apple Push Notification service (APNs).

In theory, Google could release a version of Chrome via the OS X App Store, and as a registered developer, leverage APNs, essentially creating Chrome Push Notifications (CPN). Similar to Apple, Google would have to provide their own developer console for 3rd parties to register their web site / application for sending CPNs. Doing this would allow Google to revoke anyone abusing the service. Google would host servers to receive CPNs, which in turn would forward the messages to Apple's APNs and off to Chrome running on the OS X. I don't expect we'll see Google supporting this anytime soon, as it's exclusively an OS X technology. An alternative is Google could run their own daemon on OS X (and other platforms) to receive push notifications and wake up Chrome.

Chrome has recently added Push Messaging and Notifications to Chrome across all Desktop platforms and Android. It uses Google's Cloud Messaging Platform and not Apple's default APN service, notifications that you create also will not be system level notification, but rather will appear in the little Chrome Bell icon at the top of the screen.