Can I major in chemistry in college and then go onto med school to be an anesthesiologist?

You can major in anything as long as you take the premed classes.

Pre-med is not a major. It is simply a set of required classes that you must take in order to be effectively prepared for the MCAT and medical school. You still need to major in something else. Most people major in biology or chemistry, because there is a lot of overlap between the required classes for your major and the required pre-med classes.

You can major in anything as long as you take these classes:

1 year of biology with lab

1 year of general chemistry with lab

1 year of physics with lab

1 year of organic chemistry with lab

1 year of english

Those are just the general requirements, but many schools are starting to require a year of calculus, and classes in biochemistry, physiology, or anatomy.

I have known history and music education majors that have gone to medical schools, so you are fine with a chem major.

Yes you are, a chem major is generally prefered, you just have to make sure that you get a good amount of biology in. Otherwise, even if you get in, it may be over your head. The truth is you can major in anything and go to med school, even things like art and Spanish, as long as you have the basic requirements for sciences and maths you're fine.