I saw in an article a list that implied that in Illinois it is illegal for parents to leave any of their children unsupervised at any time by an adult if the child is under 14 years of age.
Is this true?
The claim is probably based on this language from the Illinois Statutes:
§ 2-3. Neglected or abused minor.
(1) Those who are neglected include:
(d) any minor under the age of 14 years whose parent or other person responsible for the minor's welfare leaves the minor without supervision for an unreasonable period of time without regard for the mental or physical health, safety, or welfare of that minor;
So no, it is not always illegal to leave a child under 14 unsupervised; however, it is illegal (or at least considered neglect) if the child is unsupervised "for an unreasonable period of time".
What that means in practice probably depends on the interpretation of courts and child protection agencies...