Me
Actually, it takes a lot of people to research new drugs. As far as chemistry goes, they are mostly medicinal chemists or synthetic organic chemists. Chemical engineers don't usually get involved until a drug candidate has been identified and it needs to be scaled up for clinical trials.
I know that there are some people trained as pharmacists that are hired by the large pharmaceutical companies, but I'm really not sure where they are in the drug discovery process. My guess would be someplace in the pharmacodynamic and pharmacokinetic side of
in vivo testing, evaluating exposure of animals to the drug and translating that to their expected effect in humans.