Any chalk paint experts that can help with advice on an oil stain?

[Bobowhite]

I have a chest of drawers that I bought that had been painted with Annie Sloan French Linen. I thought it was sealed but some oil based moisturiser has spilt on it and has caused a huge stain. I've tried lifting the oil with heat and tea towel, no joy. And also tried sanding it but it's so oily it just makes and weird paste mess! I tried painting over it but the oil seeps through.

Any advice please? It looks awful