"Chemical accuracy" in computational chemistry, is commonly understood to be $1~\mathrm{kcal\over mol}$, or about $4~\mathrm{kJ\over mol}$. Spectroscopic accuracy is $1~\mathrm{kJ\over mol}$, and that definition has intuitive sense. However, where does the $1~\mathrm{kcal\over mol}$ quantity come from?
From Wikipedia:
A particularly important objective, called computational thermochemistry, is to calculate thermochemical quantities such as the enthalpy of formation to chemical accuracy. Chemical accuracy is the accuracy required to make realistic chemical predictions and is generally considered to be 1 kcal/mol or 4 kJ/mol.