The Chiefs will be releasing their 2011 regular season schedule on Tuesday night and it's unlikely that the Royals schedule will affect it much. The two teams share a parking lot so they usually don't play at the same time.
The NFL season is expected to start on Sunday, Sept. 11. The Royals are away that day, then home the next weekend and away the next weekend. So in what would be Week 2 of the NFL season the Chiefs may be playing an away game or a primetime game because the Royals are scheduled for a 1:10 p.m. start.
That said, there is precedent for the Royals to change their game time to accomodate the Chiefs. The NFL last year gave the Chiefs a Monday Night Football game to kick off the season and the Royals were scheduled to have a game that evening as well. So the Royals moved their game up several hours creating more room for the Chiefs MNF game.
The Chiefs schedule will be released at 6:00 p.m. (CT) Tuesday evening.