The 10km (6.2-mile) stretch of elevated track has seven stations and connects Alandur to Koyambedu.
The journey takes 15 minutes - the metro is expected to ease traffic congestion.
The construction is part of a proposed 45km (27-mile) network which is due to be completed by 2015.
Chennai is the sixth Indian city to have the metro after Delhi, Kolkata, Bangalore, Mumbai and Jaipur.
The Chennai metro was inaugurated on Monday by Tamil Nadu Chief Minister J Jayalalitha.
The first train was driven by a 28-year-old woman, A Preethi, an engineering diploma holder, reports say.
"I am excited, my daughter's dream of becoming a loco pilot (driver) of Metro Rail has come true," Ms Preethi's father R Anbu told Press Trust of India news agency.
"She quit her first job, applied for a job in Chennai metro rail, and she was the first woman to get selected. Three other women joined as pilots after her and I am happy that she was successful," he said.
The 45km (27 miles)-long, 32-station service will eventually run on two corridors in the city:  Washermenpet to Chennai Airport and Chennai Central to St Thomas Mount.
A journalist tweeted about her first experience on the service:

Gotabhaya Rajapaksa is charged with allowing a private firm to establish a floating armoury.
It is claimed the move deprived the state of more than $75m (Â£57m).
Mr Rajapaksa, who denies wrongdoing, served as defence secretary during the presidency of his brother, Mahinda Rajapaksa, which ended last year.
The charges were filed in a Colombo magistrates court by a special anti-corruption commission.
The discovery of the floating arsenal off southern Sri Lanka, and of another weapons haul in the capital, came in the days after Mahinda Rajapaksa was voted out of office.
Rajapaksa family's crashing fall from grace
Private firm Avant-Garde Security Service said the weapons were for escorting commercial ships, but police said they received complaints that the firearms were used for intimidation.
Gotabhaya Rajapaksa has also been dogged by accusations, which he denies, of human rights abuses linked to the final defeat of Tamil Tiger militants in 2009.
Several other members of the Rajapaksa family are also under investigation over alleged corruption.
Earlier this month, Namal Rajapaksa, the eldest son of Mahinda, was arrested on suspicion of money-laundering. He denies wrongdoing.
Namal's brother, Yoshitha, faces money-laundering charges while Mahinda's other brother, Basil, the former economic development minister, has been arrested three times over suspected misuse of funds and money-laundering. He is currently on bail.
Sri Lankan President Maithripala Sirisena has promised to investigate claims that members of the Rajapaksa family siphoned off billion of dollars of public money during Mahinda's nearly 10-year presidency.
The former president, now an opposition lawmaker, has also been heavily criticised over alleged human rights abuses by the Sri Lankan military during a long-running war with Tamil separatists.

The 37-year-old made 64 appearances for his country, including three at the 2006 World Cup, and is Poland's most-capped goalkeeper.
Boruc has been mainly used as a back-up keeper to Lukasz Fabianski and Wojciech Szczesny in recent years.
"It has not been an easy decision for me and has been one that I've taken incredibly seriously," he said.
"However, after much thought and consideration I feel that now is the right time in order to focus fully both on my family and club career at AFC Bournemouth."
A metro rail service has been launched in the southern Indian city of Chennai, making it the sixth Indian city to get the service.
[NEXT_CONCEPT]
One of Sri Lanka's most controversial politicians has been charged with corruption involving the illegal transfer of state-owned weapons.
[NEXT_CONCEPT]
Bournemouth's Polish goalkeeper Artur Boruc has announced his retirement from international football.