Recent neutron scattering and specific heat studies on the pyrochlore Yb2Ti2O7 have revealed variations in its magnetic behavior below 265mK. In the best samples, a sharp anomaly in the specific heat is observed at T=265mK. Other samples, especially single crystals, have broad features in the specific heat which vary in sharpness and temperature depending on the sample, indicating that the magnetic ground state may be qualitatively different in such samples. We performed detailed comparisons of the chemical structure of a pulverised single crystal of Yb2Ti2O7, grown by the floating zone technique, to a sintered powder sample of Yb2Ti2O7. Rietveld refinements of neutron powder diffraction data on these samples reveal that the crushed single crystal is best described as a "stuffed" pyrochlore, Yb2(Ti2−xYbx)O 7−x/2 with x = 0.046(4), despite perfectly stoichiometric starting material. Substituting magnetic Yb 3+ on the non-magnetic Ti 4+ sublattice would introduce random exchange bonds and local lattice deformations. These are expected to be the mechanism leading to of the variation of the delicate magnetic ground state of Yb2Ti2O7. Determination of the cubic cell length, a, could be useful as a method for characterizing the stoichiometry of nonpulverised single crystals at room temperature.PACS numbers: