  Topological insulators can be generally defined by a topological field theory
with an axion angle theta of 0 or pi. In this work, we introduce the concept of
fractional topological insulator defined by a fractional axion angle and show
that it can be consistent with time reversal (T) invariance if ground state
degeneracies are present. The fractional axion angle can be measured
experimentally by the quantized fractional bulk magnetoelectric polarization
P_3, and a `halved' fractional quantum Hall effect on the surface with Hall
conductance of the form (p/q)(e^2/2h) with p,q odd. In the simplest of these
states the electron behaves as a bound state of three fractionally charged
`quarks' coupled to a deconfined non-Abelian SU(3) `color' gauge field, where
the fractional charge of the quarks changes the quantization condition of P_3
and allows fractional values consistent with T-invariance.
