If you are able to have both a Chemistry and Chemical Engineering degree (either ungraduate or graduate), the two degree's definately work well together. If you are able to get two degrees, I would definately recommend it. The industry can never determine the next job downturn, and it is always good to have as many job options available.
Back in the old-days, you could work with one employer for your entire life. This is no longer the case. You need to make sure that you have a diverse background.
I hope this helps,