Let $ X_1, X_2,\ldots$ be a sequence of free identically
distributed random variables, with common distribution $\mu$. It was shown by
Lindsay and Pata, in a more general context, that a sufficient condition for
the weak law of large numbers to hold for the sequence $X_1, X_2,\ldots$ is
that
$$\lim_{t\to \infty}t\mu(\{x: |x|>t\}) = 0>$$
We show that this condition is necessary as well as sufficient.
Even though the condition is identical with the corresponding one for commuting
independent variables, the proof of the result uses the analytical techniques
of free convolution theory, and it is quite different from the proof of the
commutative theorem due to Kolmogorov.