According to producer Wonbo Woo at ABC News, the World News with Charles Gibson feature filmed last week is scheduled to air tomorrow, Monday, June 15th. It is a national news broadcast, so make sure to check your local listings for time and channel. In the New York tri-state area, it will air at 6:30 PM on ABC, Channel 7.
UPDATE: Here is the piece that ran as scheduled on June 15th.
Check out the ABC World News blog for an amazing promotional write-up for the show from Wonbo, or read the screencap below. Keep in mind when you're reading, the World News feature was originally supposed to air the day after Nightline but was postponed. So don't get confused, it is scheduled to air tomorrow!