Matter with a high energy density (>10(5) joules per cm(3)) is prevalent throughout the Universe, being present in all types of stars(1) and towards the centre of the giant planets(2,3); it is also relevant for inertial confinement fusion(4). Its thermodynamic and transport properties are challenging to measure, requiring the creation of sufficiently long-lived samples at homogeneous temperatures and densities(5,6). With the advent of the Linac Coherent Light Source (LCLS) X-ray laser(7), high-intensity radiation (>10(17) watts per cm(2), previously the domain of optical lasers) can be produced at X-ray wavelengths. The interaction of single atoms with such intense X-rays has recently been investigated(8). An understanding of the contrasting case of intense X-ray interaction with dense systems is important from a fundamental viewpoint and for applications. Here we report the experimental creation of a solid-density plasma at temperatures in excess of 10(6) kelvin on inertial-confinement time-scales using an X-ray free-electron laser. We discuss the pertinent physics of the intense X-ray-matter interactions, and illustrate the importance of electron-ion collisions. Detailed simulations of the interaction process conducted with a radiative-collisional code show good qualitative agreement with the experimental results. We obtain insights into the evolution of the charge state distribution of the system, the electron density and temperature, and the time-scales of collisional processes. Our results should inform future high-intensity X-ray experiments involving dense samples, such as X-ray diffractive imaging of biological systems, material science investigations, and the study of matter in extreme conditions.