A Giant Step in Cloning
I work for the company (CRi) that produced the polarized light imaging system (Oosight) that this guy credits for much of this new cloning success. In case anyone's interested the product website is here. and has links to movies of actual monkey eggs being manipulated and having their original DNA removed.
The basic principle is that the highly-ordered molecules on which the chromosomes are mounted are birefringent (they change the polarization-state of light), so if you know what the original polarization state was and if you can measure the state afterwards, then you can detect those molecules, even though they are transparent. As the BBC article says, this means you don't need to use toxic dyes to find them (which is obviously a bad idea, if you want the egg to actually survive the process).