@trimbleirl Yes, you only get one first of the day from scenarios. We want heroics as a replacement option not something else to have to do.- Greg Street (@Ghostcrawler) May 24, 2013
So, to restate what Ghostcrawler is saying, if you run a normal scenario and receive the chest, then run a heroic scenario, you will not receive a second chest. You only receive the chest from your first scenario of the day, regardless of whether that scenario is normal or heroic.
If you're after the superior chest, therfore, along with the superior rewards, you should ensure that your first scenario of the day is one of the new heroic ones. For clarity, these require a pre-made group of three, as well as an item level of 480 or above. The chest has a chance to contain ilvl 516 loot, so definitely bear this advice in mind when you're making your decisions on what you're doing today. The system seems a little counter-intuitive, so spread the word.
Update: This has now been fixed. You will receive both caches on any given day.