Can I major in nutrition with no chemistry background?

Depends on the school. Ask them about their programs. Often you can study chemistry requirements at the same places that offer degrees that require chemistry, and usually that’s not an unexpected thing to have to do. Often there’s an aptitude test they have to see whether you need to take various required classes, and at what level.

You’ll probably have to take Organic Chemistry as part of the major, but not as a prerequisite to being admitted to the program.

What @zenvelo said. Nutrition is all about the chemicals in the foods and the effects they have on the body.

You can probably learn what you need to know ad hoc, as long as you’re the sort who readily looks stuff up. I use wikipedia all the time for this. In fact wikipedia has a feature now where you can just hover your cursor over a term/link and the first paragraph or so of the main article pops up without even having to click on it. Often this is enough to keep going with what you were reading in the main wikipedia article. But, if not, you can just click on the linked article and read until you feel versed enough, and then return to the main one and to your studies. Anyway, again, that’s what I do for… well… everything! And though I had chem, bio, organic, biochem, physics, math, physiology, molecular biology, etc., I’ve forgotten probably much more detail than I’ve remembered! Plus, all that so-so-long-ago university education is way, way out of date now w/r to current research. So wikipedia to the rescue, is my rule of thumb!

No. You need to know some chemistry.