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The effects of randomly pinning particles in a model glass-forming fluid are studied, with a focus on the dynamically heterogeneous relaxation in the presence of pinning. We show how four-point dynamical correlations can be analyzed in real space, allowing direct extraction of a length scale that characterizes dynamical heterogeneity. In the presence of pinning, the relaxation time of the glassy system increases by up to two decades, but there is almost no increase in either the four-point correlation length or the strength of the four-point correlations. We discuss the implications of these results for theories of the glass transition.