  We present an analytic method for calculating the late-time tails of a linear
scalar field outside a Kerr black hole. We give the asymptotic behavior at
timelike infinity (for fixed $r$), at future null infinity, and along the event
horizon (EH). In all three asymptotic regions we find a power-law decay. We
show that the power indices describing the decay of the various modes at fixed
$r$ differ from the corresponding Schwarzschild values. Also, the scalar field
oscillates along the null generators of the EH (with advanced-time frequency
proportional to the mode's magnetic number $m$).
