The retooled Premium 360, with HDMI connector, will sport an HDMI logo on the outside of the box.

"Yes, we are offering an HDMI port for Xbox 360 simply as another choice in Xbox 360 owners' games and entertainment experience. Retailers are gradually introducing HDMI-enabled Xbox 360s into the channel to meet demand." according to a Microsoft rep.

2 days ago there were already rumours about a HDMI connector on all Xbox 360s It's still not known if the Core version will have a HDMI connector.