Can Chandra, Acolyte of Flame cast Heartfire without the additional cost?
Chandra's ability does nothing to change the total cost of Heartfire, which includes sacrificing a creature.


  You may cast target instant or sorcery card with converted mana cost 3 or less from your graveyard. If that card would be put into your graveyard this turn, exile it instead.


Note that it doesn't modify the costs, only where you can cast the card from (in this case, allowing you to cast it from your graveyard).  Compare the phrasing to Aluren, which allows you to cast specific creature cards for free.


  Any player may cast creature spells with converted mana cost 3 or less without paying their mana costs and as though they had flash.


Note that even if Chandra had the phrase "without paying it's mana cost" you would still have to sacrifice the creature as the sacrifice is an additional cost, not a mana cost.