The Tolkappiyam is a work of grammar. It is an ancient Tamil text that serves as a guideline for the grammar and structure of the Tamil language. The Tolkappiyam is considered one of the most important works in Tamil literature and is often referred to as the oldest existing work of Tamil grammar.

Option 2, A Tamil poem in praise of Rajendra Chola, is not correct. The Tolkappiyam is not a poem dedicated to a specific individual, but rather a comprehensive guide to understanding and using the Tamil language.

Option 3, An ancient didactic work in Tamil, is partially correct. The Tolkappiyam can be considered a didactic work as it provides instruction and guidance on the rules and principles of Tamil grammar. However, it is more specifically a work of grammar rather than a general didactic text.

Option 4, A drama composed by a Chera King, is not correct. The Tolkappiyam is not a drama and there is no evidence to suggest that it was composed by a Chera King.

Therefore, the correct answer is option 1, A work of grammar.