The Russian Chakvetadze, the event's top seed, needed little more than an hour in her 6-1, 6-3 victory against French wild card Nathalie Dechy.
"I wasn't expecting such an easy match," Chakvetadze admitted.
The 6th-seeded Mauresmo, a fan favorite, was leading Greece's Eleni Daniilidou 3-0 in the opening set when her opponent retired after only 10 minutes because of a viral illness.
Elsewhere, No. 2 Daniela Hantuchova of Slovakia beat Katarina Srebotnik of Slovenia 6-4, 1-6, 6-3; No. 3 Marion Bartoli of France downed rising Slovakian star Dominika Cibulkova 7-5, 6-1; France's Virginie Razzano beat compatriot Alize Cornet 6-4, 7-5, while Ukraine's Kateryna Bondarenko was an easy 6-0 6-3 winner against Yuliana Fedak.
Celebrity Families of 2014 [PHOTOS]