Will an internship in biology benefit me when my major is not biology?
I completed undergraduate summer internships in biology although I ultimately wound up applying (and attending) graduate school in psychology. Although the internship did not directly align with my current career path, at the time it helped me narrow down my professional interests. In applying for jobs and graduate school, my internships, regardless of discipline, were seen as evidence that I was motivated, organized, and had some experience in professional settings. 

At the undergraduate level many skills (including solid record keeping, attention to detail, and proper lab technique) are transferable across scientific disciplines. Further, completing one internship outside your discipline shouldn't significantly stunt your ability to prepare for graduate school in chemistry.

Having a letter of support from any professor should be acceptable, provided it is a strong letter. In all likelihood, your advisor will know you the best and be able to write the most supportive letter. However, if a life sciences professor knows you well, a second letter or co-written letter might be helpful.