Which undergraduate major leads to a research career in development of new medical drugs?
There isn't a single "correct" undergraduate major for people interested in research careers in this field. Any of biology, biochemistry, biomedical science, chemistry, pharmacology, and several others would be fine.

Much more important than finding an undergraduate degree with the right "name" would be finding a program where students have the opportunity to carry out undergraduate research with faculty doing the kind of research you want to do. 

For example, the profile of the Einstein 2016 incoming PhD class in biomedical science includes the following range of undergraduate majors:


  Undergraduate majors: Biology, Biochemistry, Biological Sciences, Microbiology, Biochemistry and Molecular Biophysics, Molecular Biology, Biotechnology, Chemistry, Genetics, and Learning Sciences


But all had a lot of prior research experience:


  100% have had a sustained research experience in a scientific laboratory
  
  57% have published a scientific paper in a peer reviewed journal
  
  65% have presented their work at a scientific meeting
  
  31% have also spent a summer in a research program
  
  Mean Months of Prior, Full‐Time Research Experience: 32