A new apparatus has been constructed which will ultimately facilitate the study of rock anelasticity under conditions which closely approach those of teleseismic wave propagation: simultaneous high pressure and temperature, low frequency and strain amplitude, and controlled pore pressure of volatiles. Its performance has been tested in a series of preliminary experiments conducted at room temperature. Measurements on a steel standard demonstrate the sensitivity of the apparatus to very small departures from ideal elasticity (Q>1000). Experimental data for a fine-grained granitic rock show that both the shear modulus G and quality factor Q increase sharply with increasing pressure below ~100 MPa, beyond which pressure both parameters become markedly less pressure sensitive. These observations are in accord with those of previous studies at higher frequencies and larger strains, and are consistent with the view that the anelasticity of rocks at ambient pressure is dominated by mechanisms operative at open cracks and grain boundaries.