Abstract: Despite the fact that latent heating in cloud systems drives many atmospheric circulations, including tropical cyclones, little is known of its magnitude and structure, largely because of inadequate observations. In this work, a reasonably high-resolution (2 km), four-dimensional airborne Doppler radar retrieval of the latent heat of condensation/evaporation is presented for rapidly intensifying Hurricane Guillermo (1997). Several advancements in the basic retrieval algorithm are shown, including (1) analyzing the scheme within the dynamically consistent framework of a numerical model, (2) identifying algorithm sensitivities through the use of ancillary data sources, and (3) developing a precipitation budget storage term parameterization. The determination of the saturation state is shown to be an important part of the algorithm for updrafts of ~5 m s^-1 or less. The uncertainties in the magnitude of the retrieved heating are dominated by errors in the vertical velocity. Using a combination of error propagation and Monte Carlo uncertainty techniques, biases are found to be small, and randomly distributed errors in the heating magnitude are ~16% for updrafts greater than 5 m s^-1 and ~156% for updrafts of 1 m s^-1. Even though errors in the vertical velocity can lead to large uncertainties in the latent heating field for small updrafts/downdrafts, in an integrated sense the errors are not as drastic. In Part II, the impact of the retrievals is assessed by inserting the heating into realistic numerical simulations at 2-km resolution and comparing the generated wind structure to the Doppler radar observations of Guillermo.