Are there any harmful chemicals in plastic water jugs that might hurt a child?

Yes. Plastic water bottles, and many other stiff plastic bottles, often contain a chemical called bpa which can leach into the water and can be pretty toxic. Recent media attention has led many of the manufacturers of this plastic to replace those bottles with others that are bpa free. There is increasing information that the replacements might not be much better. Filter your own water to be safe.
Plastic chemicals. Some people are worried about the effects of chemicals in plastics such as bisphenol a, especially on children because they are more sensitive to things than adults as they are developing. There is controversy over these chemicals. To be safe, look for bpa-free bottles and never heat or microwave food/drink in plastic containers as that releases bpa.