Chu's limit determines the minimum radiation quality factor Q of an electrically small resonator, and hence its maximum operational bandwidth, which is inversely proportional to its volume. This bound imposes severe restrictions in several areas of technology, from wireless communications to nanophotonics and metamaterials. We show that a suitably tailored temporal modulation of the matching network, combined with proper detuning of the feeding impedance, can overcome this limit and enable radiation over broader bandwidths, which scale as 1/sqrt[Q], ensuring at the same time stability. Our findings open opportunities for communication systems, nanophotonics, and sensor technology.