  The Brownian loop soup introduced in Lawler and Werner (2004) is a Poissonian
realization from a sigma-finite measure on unrooted loops. This measure
satisfies both conformal invariance and a restriction property. In this paper,
we define a random walk loop soup and show that it converges to the Brownian
loop soup. In fact, we give a strong approximation result making use of the
strong approximation result of Koml\'os, Major, and Tusn\'ady. To make the
paper self-contained, we include a proof of the approximation result that we
need.
