  Turbulence is one of the most fascinating phenomena in nature and one of the
biggest challenges for modern physics. It is common knowledge that a flow of a
simple, Newtonian fluid is likely to be turbulent, when velocity is high,
viscosity is low and size of the tank is large\cite{Landau,Tritt}. Solutions of
flexible long-chain polymers are known as visco-elastic fluids\cite{bird}. In
our experiments we show, that flow of a polymer solution with large enough
elasticity can become quite irregular even at low velocity, high viscosity and
in a small tank. The fluid motion is excited in a broad range of spatial and
temporal scales. The flow resistance increases by a factor of about twenty. So,
while the Reynolds number, $\boldmath{Re}$, may be arbitrary low, the observed
flow has all main features of developed turbulence, and can be compared to
turbulent flow in a pipe at $\bf {Re\simeq 10^5}$\cite{Landau,Tritt}. This {\it
elastic turbulence} is accompanied by significant stretching of the polymer
molecules, and the resulting increase of the elastic stresses can reach two
orders of magnitude.
