Chakvetadze posted a 6-4, 6-0 victory over Tatiana Poutchek of Belarus, while Schnyder defeated Austrian Monique Adamczak 6-2, 7-5.
In an upset, unseeded-Georgian Anna Tatishvili beat fifth-seeded Aiko Nakamura 1-6, 6-4, 7-6 (7-4).
In other matches, sixth-seeded Russian Elena Vesnina defeated Germany's Angelika Bachmann 6-3, 6-4; American Jill Craybas beat countrywoman Alexa Glatch 6-2, 6-4; Romania's Anda Perianu beat Hungary's Melinda Czink 6-3, 6-2; and Varvara Lepchenko of Uzbekistan defeated American Kirsten Flower 6-2, 6-2.
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