The correct answer is A. 1.00 gram.
One mole of any substance contains 6.02214076 x 10^23 atoms or molecules. The atomic mass of helium is 4.002602 u. Therefore, the mass of one mole of helium is 4.002602 grams. Since one mole is equal to 6.02214076 x 10^23 atoms, the mass of one Avogadro number of helium atoms is 4.002602 / 6.02214076 x 10^23 = 0.06646476 x 10^-23 grams = 1.00 grams.
Option B is incorrect because it is twice the mass of one mole of helium. Option C is incorrect because it is four times the mass of one mole of helium. Option D is incorrect because it is not a meaningful unit of mass.