  Exceptional points (EPs)--singularities in the parameter space of
non-Hermitian systems where two nearby eigenmodes coalesce--feature unique
properties with applications for microcavity lasers such as sensitivity
enhancement and chiral emission. Present EP lasers operate with static
populations in the gain medium. Here, we show theoretically that a laser
operating sufficiently close to an EP will spontaneously induce a
multi-spectral multi-modal instability that creates an oscillating population
inversion and generates a frequency comb. The comb formation is enhanced by the
non-orthogonality of modes via the Petermann factor. Such an "EP comb" features
an ultra-compact size and a widely tunable repetition rate, without requiring
external modulators or a continuous-wave pump. We develop an exact ab initio
dynamic solution of the space-dependent Maxwell-Bloch equations, describing all
steady-state properties of the EP comb. We illustrate this phenomenon in a
realistic parity-time-symmetric 5-{\mu}m-long AlGaAs cavity and validate our
prediction with finite-difference time-domain simulations. This work reveals
the rich physics that connect non-Hermitian degeneracies and the nonlinear
dynamics of gain media to fundamentally alter the laser behavior.
