We use confocal microscopy to visualize individual particles near the colloidal glass transition. We identify the most slowly-relaxing particles and show that they form spatially correlated clusters that percolate across the sample. In supercooled fluids, the largest cluster spans the system on short time scales but breaks up on longer time scales. In contrast, in glasses, a percolating cluster exists on all accessible time scales. Using molecular dynamics simulation, we show that these clusters make the dominant contribution to the bulk elasticity of the sample.