Q. In formal writing, I have been shown by my coworkers that U.S. is the way to write United States. However, I was always told that very few abbreviations are to be used in formal writing, and the abbreviation U.S. should never be used in replacement of United States when writing federal documents.
A. If you type United States into our Search box, the first hit takes you to CMOS 10.33. (You can also find this in the index.) Chicago style is to spell out the noun in running text, but abbreviate the adjective as US. (Note that the federal government doesn’t necessarily follow Chicago style, however!)