Mailing chicks via USPS [1] is legal and common:

    Some animals are mailable under proper conditions. See the specific         
    instructions as noted for the following kinds of animals:

    * Live bees
    * Live, day-old poultry
    * Live adult fowl
    * Live scorpions (only under limited circumstances)
    * Other small, harmless, cold–blooded animals

[1] http://pe.usps.gov/text/pub52/pub52c5_008.htm