Inelastic neutron scattering data from a twinned single-crystal of YBa2Cu3O6.95 are presented that show a distinct a-b plane anisotropy in the oxygen vibrations. The Cu-O bond-stretching type phonons are simultaneously observed along the a and b directions due to a 4 meV splitting arising from the orthorhombicity. The present results show the bond-stretching branch along b (parallel to the chain) has a continuous dispersion, while the branch along a is discontinuous, suggesting a possibility of short-range cell-doubling along a. Furthermore, the LO mode along a is split in en-ergy from its TO partner at non-zero q-vectors, while the b mode is not. These results imply strong anisotropy in the electronic screening and a one-dimensional character in underlying charge fluctuations.