The correct chronological order of the Sanskrit grammarians mentioned in the question is 1-2-3, which means that Panini came before Katyayana and Patanjali. Let's delve into the details to understand why this is the correct order.

1. Panini:
Panini is considered the most important and influential Sanskrit grammarian in the history of ancient India. He is believed to have lived around the 4th century BCE. Panini's work, known as Ashtadhyayi, is a comprehensive and systematic treatise on Sanskrit grammar. It consists of around 4,000 rules organized in eight chapters. Panini's grammar is highly scientific and precise, providing a framework for the analysis, derivation, and composition of Sanskrit words. His work laid the foundation for the development of Sanskrit linguistics and influenced subsequent grammatical studies.

2. Katyayana:
Katyayana, also known as Mahakatyayana, was a disciple of Panini. He lived around the 3rd century BCE and is recognized as one of the important Sanskrit grammarians. Katyayana wrote a commentary on Panini's Ashtadhyayi called Varttika. This commentary elucidates and expands upon the rules and concepts mentioned by Panini. Katyayana's Varttika is considered a significant work that helps in understanding and interpreting Panini's grammar more comprehensively.

3. Patanjali:
Patanjali is believed to have lived around the 2nd century BCE and is known for his work on grammar called Mahabhashya. Patanjali's Mahabhashya is a commentary on Katyayana's Varttika, which, in turn, is a commentary on Panini's Ashtadhyayi. Mahabhashya is a comprehensive and detailed analysis of the Sanskrit language, covering various aspects of grammar, semantics, and philosophy. Patanjali's work is highly regarded for its scholarly insights and critical examination of earlier grammatical works.

In summary, Panini, Katyayana, and Patanjali are important Sanskrit grammarians who made significant contributions to the development and understanding of Sanskrit grammar. Panini's Ashtadhyayi laid the foundation, Katyayana's Varttika provided further explanation, and Patanjali's Mahabhashya analyzed and interpreted the earlier works. Therefore, the correct chronological order of these grammarians is 1-2-3, as mentioned in option A.