NOAA/NCEI U.S. Climate Division Data Plotting Page: Division boundaries and county relationships.
NCEI provides a link to their climate division shapefiles (zipped). Please email them with questions. email@example.com.
NCAR has a netCDF file with the climate division boundaries available entitled "climdiv_polygons.nc". NCL has the boundaries builtin to its plotting code as does GrADS.
You can find the counties that are in each division using this table provided by NCEI.