The Lausanne-based court suspended the governing International Association of Athletics Federations' (IAAF) regulations regarding hyperandrogenism, a condition which produces high testosterone levels, for two years.
It cleared the way for Chand to compete again in both domestic and international events after she was forced to sit out about a year of competition.
She clocked a national record 11.30 seconds in the 100m heats at the G. Kosanov Memorial Meet in Almaty, Kazakhstan, to qualify for the Rio Games, the qualifying mark for which was set at 11.32.
"I am really happy at the moment," she said in a statement. "It has been a tough year for me and I am so happy that my coach ... and my hard work has paid off.
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"I would like to thank all the people in India who were praying for me to qualify. Your wishes have paid off."
The daughter of a weavers from the eastern Indian state of Orissa, Chand was dropped from India's contingent for the Glasgow Commonwealth Games and the Asian Games in Incheon after her naturally-occurring testosterone levels were found to be in breach of IAAF's guidelines.
She was advised to have surgery and take medication but instead decided to challenge the guidelines at CAS, who asked the IAAF to present scientific evidence proving enhanced testosterone levels improved performance in hyperandrogenic athletes.
South Africa's former world champion 800m runner Caster Semenya was also subjected to gender testing by the IAAF before being cleared to compete as a woman.
The Rio Olympics take place from Aug. 5-21.
(Reporting by Sudipto Ganguly; editing by Nick Mulvenney)
