  The evidence for supermassive Kerr black holes in galactic centers is strong
and growing, but only the detection of gravitational waves will convincingly
rule out other possibilities to explain the observations. The Kerr spacetime is
completely specified by the first two multipole moments: mass and angular
momentum. This is usually referred to as the ``no-hair theorem'', but it is
really a ``two-hair'' theorem. If general relativity is the correct theory of
gravity, the most plausible alternative to a supermassive Kerr black hole is a
rotating boson star. Numerical calculations indicate that the spacetime of
rotating boson stars is determined by the first three multipole moments
(``three-hair theorem''). LISA could accurately measure the oscillation
frequencies of these supermassive objects. We propose to use these measurements
to ``count their hair'', unambiguously determining their nature and properties.
