  We present a detailed analysis of the connection between chaos and the onset
of thermalization in the spin-boson Dicke model. This system has a well-defined
classical limit with two degrees of freedom, and it presents both regular and
chaotic regions. Our studies of the eigenstate expectation values and the
distributions of the off-diagonal elements of the number of photons and the
number of excited atoms validate the diagonal and off-diagonal eigenstate
thermalization hypothesis (ETH) in the chaotic region, thus ensuring
thermalization. The validity of the ETH reflects the chaotic structure of the
eigenstates, which we corroborate using the von Neumann entanglement entropy
and the Shannon entropy. Our results for the Shannon entropy also make evident
the advantages of the so-called "efficient basis" over the widespread employed
Fock basis when investigating the unbounded spectrum of the Dicke model. The
efficient basis gives us access to a larger number of converged states than
what can be reached with the Fock basis.
