  The scrambling rate $\lambda_L$ associated with the exponential growth of
out-of-time-ordered correlators can be used to characterize quantum chaos. Here
we use the Majorana Fermion representation of spin $1/2$ systems to study
quantum chaos in the Dicke model. We take the system to be in thermal
equilibrium and compute $\lambda_L$ throughout the phase diagram to leading
order in $1/N$. We find that the chaotic behavior is strongest close to the
critical point. At high temperatures $\lambda_L$ is nonzero over an extended
region that includes both the normal and super-radiant phases. At low
temperatures $\lambda_L$ is nonzero in (a) close vicinity of the critical point
and (b) a region within the super-radiant phase. In the process we also derive
a new effective theory for the super-radiant phase at finite temperatures. Our
formalism does not rely on the assumption of total spin conservation.
