Attachment of spindle fibers to kinetochores of chromosomes becomes evident in:

Metaphase:
• All the chromosomes come to lie at the equator. 
• In each chromosome, one chromatid is connected to the spindle fibre from one pole and another chromatid is connected to the spindle fibre from another pole. The spindle fibres attach to the kinetochore of the centromere, and it becomes evident due to the alignment of chromosomes in a plane. 
• The plane of alignment of chromosomes during this phase is called the metaphase plate.