Dr. and Mrs. Randolph Chick of Fayetteville announce the engagement of their daughter, Zoe Anna Claire, to Cary Williams IV, son of Mr. and Mrs. Cary Williams III of Dallas, Texas. Miss Chick graduated from the University of Arkansas and earned a graduate degree from the University of Oklahoma. She is a Children's Librarian at Dallas Public Library. Mr. Williams received a degree in business administration from the University of Oklahoma and works for Dust Cutter Beverage Company in Dallas. An August wedding is planned.