  In a chiral superconductor with broken time-reversal symmetry a ``spontaneous
Hall effect'' may be observed. We analyze this phenomenon by taking into
account the surface properties of a chiral superconductor. We identify two main
contributions to the spontaneous Hall effect. One contribution originates from
the Bernoulli (or Lorentz) force from spontaneous currents running along the
surfaces of the superconductor. The other contribution has a topological origin
and is related to the intrinsic angular momentum of Cooper pairs. The latter
can be described in terms of a Chern-Simons-like term in the low-energy field
theory of the superconductor and has some similarities with the quantum Hall
effect. The spontaneous Hall effect in a chiral superconductor is, however,
non-universal. Our analysis is based on three approaches to the problem: a
self-consistent solution of the Bogoliubov-de Gennes equation, a generalized
Ginzburg-Landau theory, and a hydrodynamic formulation. All three methods
consistently lead to the same conclusion that the spontaneous Hall resistance
of a two-dimensional superconducting Hall bar is of order h/(e k_F\lambda)^2,
where k_F is the Fermi wave vector and \lambda is the London penetration depth;
the Hall resistance is substantially suppressed from a quantum unit of
resistance. Experimental issues in measuring this effect are briefly discussed.
