A systematic methodology for the reconstruction of climate fields from sparse observational networks of proxy data, employing the technique of reduced space objective analysis, is applied to the reconstruction of gridded Pacific Ocean Basin sea surface temperature (SST) from coral stable isotope (δ18O) data for the period 1607--1990. In this approach we seek to reconstruct only the leading modes of large-scale variability which are both observed in the modern climate and resolved in the proxy data. We find that the coral data verifiably resolve two spatial patterns of SST variability. The first and dominant pattern is that of the El Ni¿o--Southern Oscillation (ENSO). A second pattern reflects uniform changes over most of the Pacific Basin. Calibration and verification tests for 1856--1990 show that root-mean-square variance is small (≤0.5¿C RMS) and reconstruction errors are large (≤0.6¿C RMS), limiting interpretation to the tropical region. Periods of enhanced ENSO activity similar to those observed in the past two decades are evident in the reconstruction for the early nineteenth century. The changing frequency of ENSO warm phase events appears to coincide with warming of the Pacific mean state inferred from similar reconstruction efforts using tree ring indicators over the last two centuries.