We present observations of the Soft Gamma-ray Repeater SGR 1806-20 taken with the Chandra X-ray Observatory. We identify the X-ray counterpart of SGR 1806-20 based on detection of 7.5-s pulsations. Using three unrelated X-ray sources (and USNO stars) as position references, we are able to determine that the SGR is at alpha_{2000}=18h08m39.32s and delta_{2000}=-20o24'39.5", with rms uncertainty of 0.3" in each coordinate. We find that SGR 1806-20 is located within the 1-sigma error region determined by Interplanetary Network data and is 14+/-0.5 arcsec distant from the non-thermal core of SNR G10.0-0.3, excluding SGR 1806-20 as the origin of the core. We see evidence for a significant deviation of the spin-down of SGR 1806-20 from its long-term trend, demonstrating erratic spin-down behavior in this source similar to that seen in other SGRs. Finally, we show that there is a broad X-ray halo surrounding SGR 1806-20 out to radii ~1' due to scattering in the interstellar medium.