Invisibility cloaks, which used to be confined to the realm of fiction, have now been turned into a scientific reality thanks to the enabling theoretical tools of transformation optics and conformal mapping. Inspired by those theoretical works, the experimental realization of electromagnetic invisibility cloaks has been reported at various electromagnetic frequencies. All the invisibility cloaks demonstrated thus far, however, have relied on nano- or micro-fabricated artificial composite materials with spatially varying electromagnetic properties, which limit the size of the cloaked region to a few wavelengths. Here, we report the first realization of a macroscopic volumetric invisibility cloak constructed from natural birefringent crystals. The cloak operates at visible frequencies and is capable of hiding, for a specific light polarization, three-dimensional objects of the scale of centimetres and millimetres. Our work opens avenues for future applications with macroscopic cloaking devices.