The expression “chip of the old block” means one who has the characteristics of a parent, usually a son with those of his father.
The expression goes back to the early seventeenth century and, if some of the early sermons of Bishop Robert Sanderson quote it correctly, the original form showed less disrespect to dad. It ran, “chip of the same block.”
The allusion is not difficult to follow: if one takes a block of stone and knocks a chip from it, the chip will carry all the characteristics of the larger portion.