Yes — Chennai is generally considered one of India's safer major cities for tourists. Violent crime targeting visitors is rare, and the city has a comparatively conservative, community-oriented culture that tends to be hospitable toward foreigners.
Practical tips: Use Ola or Uber for all taxi journeys rather than unlicensed autos for longer trips (auto-rickshaws are fine for short hops but agree the fare upfront or insist on the meter). Keep copies of your passport and visa separately from originals. Be alert to common tourist scams such as unofficial 'guides' at temples who charge inflated fees.
Solo female travellers generally find Chennai safer than many Indian cities, but it is advisable to use app-based cabs after dark, dress modestly (especially near temples and markets), and stay in well-reviewed accommodation in areas like Nungambakkam, Adyar, or T. Nagar.
Cyclone season (October–December) occasionally brings severe weather — check India Meteorological Department alerts during the North-East Monsoon.