A few folks have mentioned to me that Mike Mearls has stated elsewhere that it's an oversight in the text, and the intent is that a level 1 character should recover 1 hit die. Seems likely errata-fodder.
@MrMattFree : Hit dice question! Basic rules say you get half your HD back at a long rest but doesn't say round up. What does a 1st lvl do?
@mikemearls : should be minimum 1.
The rules for long rests were later updated (in the 0.2 version of the Basic Rules)later updated to say that the minimum is 1 hit die.
The character also regains spent Hit Dice, up to a number of dice equal to half of the character’s total number of them (minimum of one die). (p 67PBRv0.2 p.67, PHB5e p.186)