Dual major in ChemE and Chemistry?

I'm currently a senior in high school set to graduate this year, and understandably, I'm a little nervous about my major for my first semester at school.

I applied to school as a Chemical Engineering student, with my second choice being Chemistry or Biochem. I find both fields fascinating, but I'm wondering if a dual major would be bee beneficial between Chemistry and ChemE, or even feasible? Are there many overlapping classes between the two, and would having a double major open any doors for me?

Thanks!