  We introduce an $\ell$-adic analogue of Gauss's hypergeometric function
arising from the Galois action on the fundamental torsor of the projective line
minus three points. Its definition is motivated by a relation between the
KZ-equation and the hypergeometric differential equation in the complex case.
We show two basic properties, analogues of Gauss's hypergeometric theorem and
of Euler's transformation formula for our $\ell$-adic function. We prove them
by detecting a connection of a certain two-by-two matrix specialization of even
unitary associators with the associated gamma function, which extends the
result of Ohno and Zagier.
