  The heavy fermion metal \beta-YbAlB4 exhibits a bulk room temperature
conduction electron ESR signal which evolves into an Ising-anisotropic
f-electron signal exhibiting hyperfine features at low temperatures. We develop
a theory for this phenomenon based on the development of resonant scattering
off a periodic array of Kondo centers. We show that the hyperfine structure
arises from the scattering off the Yb atoms with non zero nuclear spin, while
the constancy of the ESR intensity is a consequence of the presence of CEF
excitations of the order of the hybridization strength.
