An important strategy for realizing flexible electronics is to use solution-processable materials that can be directly printed and integrated into high-performance electronic components on plastic. Although examples of functional inks based on metallic, semiconducting and insulating materials have been developed, enhanced printability and performance is still a challenge. Printable high-capacitance dielectrics that serve as gate insulators in organic thin-film transistors are a particular priority. Solid polymer electrolytes (a salt dissolved in a polymer matrix) have been investigated for this purpose, but they suffer from slow polarization response, limiting transistor speed to less than 100 Hz. Here, we demonstrate that an emerging class of polymer electrolytes known as ion gels can serve as printable, high-capacitance gate insulators in organic thin-film transistors. The specific capacitance exceeds that of conventional ceramic or polymeric gate dielectrics, enabling transistor operation at low voltages with kilohertz switching frequencies.