DNA sequencing using solid-state nanopores is, in part, impeded by the relatively high noise and low bandwidth of the current state-of-the-art translocation measurements. In this Letter, we measure the ion current noise through sub 10 nm thick Si3N4 nanopores at bandwidths up to 1 MHz. At these bandwidths, the input-referred current noise is dominated by the amplifier’s voltage noise acting across the total capacitance at the amplifier input. By reducing the nanopore chip capacitance to the 1–5 pF range by adding thick insulating layers to the chip surface, we are able to transition to a regime in which input-referred current noise (∼117–150 pArms at 1 MHz in 1 M KCl solution) is dominated by the effects of the input capacitance of the amplifier itself. The signal-to-noise ratios (SNRs) reported here range from 15 to 20 at 1 MHz for dsDNA translocations through nanopores with diameters from 4 to 8 nm with applied voltages from 200 to 800 mV. Further advances in bandwidth and SNR will require new amplifier designs that reduce both input capacitance and input-referred amplifier noise.