Ultra-small size, high-performance, solenoid-type RF chip inductors utilizing low-loss A1$_2$O$_3$ core materials were investigated. The dimensions of the RF chip inductors fabricated were 1.0mm${ imes}$0.5mm${ imes}$0.5mm and copper coils were used. The materials (96％ A1$_2$O$_3$) and shape (I-type) of the core, the diameters (40${mu}{ extrm}{m}$) and position (middle) of the coil, and the lengths (0.35mm) of solenoid were determined by a high-frequency structure simulator (HFSS) to maximize the performance of the inductors. The high-frequency characteristics of the inductance (L) and quality-factor (Q) of the developed inductors were measured using a RF impedance/material analyzer (E4991A with E16197A test fixture). The developed inductors exhibit an inductance of 11 to 11.3nH and a qualify factor of 22.3 to 65.7 over the frequency ranges of 250 MHz to 1.7 GHz, and show results comparable to those measured for the inductors prepared by Coilcraft$^{TM}$. The simulated data described the high-frequency data of the L and Q of the fabricated inductors well.