How do I extract a single chunk of bytes from within a file?

Try dd:

dd skip=102567 count=253 if=input.binary of=output.binary bs=1

The option bs=1 sets the block size, making dd read and write one byte at a time. The default block size is 512 bytes.

The value of bs also affects the behavior of skip and count since the numbers in skip and count are the numbers of blocks that dd will skip and read/write, respectively.