Considerable excitement has been caused recently by the discovery that the binary boride system with stoichiometry MgB2 is superconducting at the remarkably high temperature of 39 K (1). This potentially opens the way to even higher Tc values in a new family of superconductors with unexpectedly simple composition and structure. The simplicity in the electronic and crystal structures could allow the understanding of the physics of high-Tc superconductivity without the presence of the multitude of complicated features, associated with the cuprates. Synchrotron X-ray diffraction was used to measure the isothermal compressibility of MgB2, revealing a stiff tightly-packed incompressible solid with only moderate bonding anisotropy between intra- and inter-layer directions. These results, combined with the pressure evolution of the superconducting transition temperature, Tc establish its relation to the B and Mg bonding distances over a broad range of values.