Yes, my pure white show cat has had it!!!
If you use plastic feeding dishes throw them away immediately, use metal ones and wash them daily at high temperature. Oils from foods can exacerbate the problem which is caused by sebaceous excretions. Switch to dry food if possible - a high quality one not cheap as chips go-cat or the like. Wash the chin area daily with a chlorhexidine based soap such as hibiscrub or betadine. Likelihood is it will also be present in the tail, can often look like flea dirt.
Express the blackheads and clean immediately after with solution as above.
It does take a while to go sadly but the bowls thing is crucial.
HTH