The correct answer is: Chennai.
Chennai is the capital of the Indian state of Tamil Nadu. It is the most populous city in the state and the fourth most populous city in India. The city has a population of over 10 million people. The population density of Chennai is 28,480 people per square kilometer. This is the highest population density of any district in Tamil Nadu.
Coimbatore is the second most populous city in Tamil Nadu. It has a population of over 3 million people. The population density of Coimbatore is 1,000 people per square kilometer. This is much lower than the population density of Chennai.
Madurai is the third most populous city in Tamil Nadu. It has a population of over 2 million people. The population density of Madurai is 1,200 people per square kilometer. This is also much lower than the population density of Chennai.
Kanchipuram is a district in Tamil Nadu. It has a population of over 3 million people. The population density of Kanchipuram is 1,000 people per square kilometer. This is much lower than the population density of Chennai.
The high population density of Chennai is due to a number of factors. First, Chennai is a major commercial and industrial center. It is home to many large companies and factories. Second, Chennai is a major port city. It is a major hub for trade and commerce. Third, Chennai is a major tourist destination. It is home to many historical and cultural sites.