I've heard that skimmed milk has more added chemicals than whole milk. Is this true?
The prescriptionist scientist in me rejects the question as meaningless! The descriptivist in me compels me to try to answer the question you meant to ask.
Both whole milk and skim milk (in the USA) may be fortified with vitamins A and/or D.
Sharon Gerdes wrote in Dairy Foods (Feb 2009):
They can also be fortified with other nutrients such as Calcium.
The fortification is optional, so it depends on the source. So, to see what additives are in your preferred brands of milk, check the labels. Before you discard the ones with more Vitamin A and D, ask if you are really concerned that the risks of extra vitamins outweigh the benefits - ditto with the fat content.
However, Cornell University's Milk Facts suggests a motivation for additional Vitamin A fortification in skim milk: because it is naturally lower in vitamin A, it needs more added to bring it to the same levels as whole milk.
Letting my inner prescriptionist off his leash for a moment:
In science, the word "chemical" means the same as chemical substance.
(Ref: High school chemistry, plus the above Wikipedia article that states: 'the term chemical substance is a precise technical term that is synonymous with "chemical" for professional chemists'.)
Under this definition, everything is either a chemical substance or a mixture of chemical substances. (Okay, not everything. Not light or heat or love or skepticism, but everything made of solids, liquids, gasses or plasma. Everything you can touch, taste or smell.)
So, 1kg of whole milk is 100% chemicals, and 1kg of skim-milk is 100% chemicals. No difference.
Skim milk is usually made by centrifugation of whole milk. Otherwise the fatty cream is allowed to rise naturally, and skimmed off. Neither process involves adding new chemicals to the milk, or anything other than separation based on physical properties. If you're counting types of chemicals in your milk, whole milk will be slightly higher, as it still contains all those fats and fat soluble materials that make up cream. As Oddthinking states, both whole and skim milk may be fortified by vitamins A and/or D.