A colloidal solution is a homogeneous dispersion of particles or droplets of one phase (solute) in a second, typically liquid, phase (solvent). Colloids are ubiquitous in biological, chemical and technological processes, homogenizing highly dissimilar constituents. To stabilize a colloidal system against coalescence and aggregation, the surface of each solute particle is engineered to impose repulsive forces strong enough to overpower van der Waals attraction and keep the particles separated from each other. Electrostatic stabilization of charged solutes works well in solvents with high dielectric constants, such as water (dielectric constant of 80). In contrast, colloidal stabilization in solvents with low polarity, such as hexane (dielectric constant of about 2), can be achieved by decorating the surface of each particle of the solute with molecules (surfactants) containing flexible, brush-like chains. Here we report a class of colloidal systems in which solute particles (including metals, semiconductors and magnetic materials) form stable colloids in various molten inorganic salts. The stability of such colloids cannot be explained by traditional electrostatic and steric mechanisms. Screening of many solute-solvent combinations shows that colloidal stability can be traced to the strength of chemical bonding at the solute-solvent interface. Theoretical analysis and molecular dynamics modelling suggest that a layer of surface-bound solvent ions produces long-ranged charge-density oscillations in the molten salt around solute particles, preventing their aggregation. Colloids composed of inorganic particles in inorganic melts offer opportunities for introducing colloidal techniques to solid-state science and engineering applications.