The deposition of clay-sized particles by settling from suspension within a water column typically forms highly porous (80%-90% water) muds dominated by uniformly distributed and randomly oriented particles. The depositional microfabric of muds is rapidly destroyed during burial, resulting in mudstones with a strong preferred particle orientation. Here we show that laminated chert in banded iron formations from the Hamersley Group, Australia, and Ghaap Group, South Africa, preserve laminae of nanometer-sized particles of greenalite with textures that resemble the fabric of freshly deposited muds-the oldest such fabrics in the rock record. The preservation of the textures implies that the nanoparticles were "frozen" by silica cement on or just below the seafloor, an interpretation supported by their presence in intraformational chert clasts and nodules with strong differential compaction. The co-occurrence of stacks of plates forming thicker aggregates with multiple face-to-edge contacts indicates that the greenalite may have been deposited as loosely formed flocs. The common occurrence, in certain horizons, of iron-silicate microgranules dispersed in the greenalite mud resembles aggregates of clay particles documented in modern muds. These textures support models for active seawater precipitation of the iron-rich phases and point to collision and flocculation of particles during sediment transport. Upon deposition, amorphous silica rapidly occluded the available porosity and entombed the precipitates in a chemically inert cement that limited burial-related compaction and hindered diagenetic reactions, providing a taphonomic view of the earliest mineralogy and texture of iron formations.