We describe a variant of the quadrupole rf (Paul) ion trap capable of localization of a trapped ion to much less than an optical wavelength (Lamb-Dicke regime). The trapping potentials are generated by a high-Q, vacuum-compatible, quarter-wave resonator driven at about 240 MHz. The binding strength of the trap has been characterized. The trap contains compensation electrodes which allow the cancellation of stray static electric fields within the trap. Secular frequencies of tens of megahertz have been achieved for trapped magnesium and beryllium ions.