The Deformation Space of Calabi-Yau n-folds with canonical singularities   can be obstructed
  This paper gives a simple example of a family of Calabi-Yaus of any dimension with canonical singularities of dimension one, whose Kuranishi space is singular. Thus the Bogomolov-Tian-Todorov unobstructedness theorem is not true for Calabi-Yaus with canonical singularities. 
Mark Gross