We use confocal microscopy to study the compressibility of a random-close-packed sample of colloidal particles. To do this, we introduce an algorithm to estimate the size of each particle. Taking into account their sizes, we compute the compressibility of the sample as a function of wave vector q, and find that this compressibility vanishes linearly as q→0, showing that the packing structure is incompressible. The particle sizes must be considered to calculate the compressibility properly. These results also suggest that the experimental packing is hyperuniform.