Explanation:

- Lucknow is the correct answer. It is famous worldwide for its Chikankari embroidery, a delicate and complex form of hand embroidery that has been practiced for centuries.

- Ahmedabad is known for its rich textile history, particularly in silk and cotton, but it is not specifically famous for Chikankari.

- Hyderabad is renowned for its beautiful pearls and rich cultural heritage, including various arts, but not specifically for Chikankari.

- Udaipur, known as the City of Lakes, is famous for its palaces and scenic beauty rather than any particular embroidery style.