In a chiral superconductor with broken time-reversal symmetry a "spontaneou
s Hall effect" may be observed. We analyze this phenomenon by taking into a
ccount the surface proper-ties of a chiral superconductor. We identify two
main contributions to the spontaneous Hall effect. One contribution origina
tes from the Bernoulli (or Lorentz) force due to spontaneous currents runni
ng along the surfaces of the superconductor. The other contribution has a t
opological origin and is related to the intrinsic angular momentum of Coope
r pairs. The latter can be described in terms of a Chem-Simons-like term in
the low-energy field theory of the superconductor and has some similaritie
s with the quantum Hall effect. The spontaneous Hall effect in a chiral sup
erconductor is, however, nonuniversal. Our analysis is based on three appro
aches to the problem: a self-consistent solution of the Bogoliubov-de Genne
s equation, a generalized Ginzburg-Landau theory, and a hydrodynamic formul
ation. All three methods consistently lead to the same conclusion that the
spontaneous Hall resistance of a two-dimensional superconducting Hall bar i
s of order h/(ek(F)lambda)(2), where k(F) is the Fermi wave vector and lamb
da is the London penetration depth; the Hall resistance is substantially su
ppressed from a quantum unit of resistance. Experimental issues in measurin
g this effect are briefly discussed.