We measured bulk and surface dielectric breakdown thresholds of pure silica for $14\mathrm{ps}$ and $8\mathrm{ns}$ pulses of $1064\mathrm{nm}$ light. The thresholds are sharp and reproducible. For the $8\mathrm{ns}$ pulses the bulk threshold irradiance is $4.75\pm 0.25\mathrm{kW}/{\mathrm{\mu m}}^2$ . The threshold is approximately three times higher for $14\mathrm{ps}$ pulses. For $8\mathrm{ns}$ pulses the input surface damage threshold can be made equal to the bulk threshold by applying an alumina or silica surface polish.