We have synthesized inorganic micron-sized filaments, whose microstucture consists of silica-coated nanometer-sized carbonate crystals, arranged with strong orientational order. They exhibit noncrystallographic, curved, helical morphologies, reminiscent of biological forms. The filaments are similar to supposed cyanobacterial microfossils from the Precambrian Warrawoona chert formation in Western Australia, reputed to be the oldest terrestrial microfossils. Simple organic hydrocarbons, whose sources may also be abiotic and indeed inorganic, readily condense onto these filaments and subsequently polymerize under gentle heating to yield kerogenous products. Our results demonstrate that abiotic and morphologically complex microstructures that are identical to currently accepted biogenic materials can be synthesized inorganically.