The office would coordinate with its Consulate office in Mumbai in issuance of visas and other services.
A 60-member delegation led by Governor of San Luis Province of Argentina, Claudio Poggi, is on a two-day visit to Chennai as part of the inauguration of the office.
After inaugurating the trade and cultural office, Tamil Nadu Governor K Rosaiah said "it's an auspicious beginning and a landmark occasion in the annals of Indo-Argentina bilateral relations.
"The bonds of friendship and cooperation between India and Argentina have developed transcending geographical boundaries", he said.
With the opening of the trade and cultural office today, he hoped it would help explore the opportunities.
Trade between India and Argentina in 2012 stood at USD 1.8 billion. India's main exports to Argentina are organic chemicals, vehicles, auto parts, lubricants, machinery while it imports soyabean oil, sunflower oil, leather, wool among others.