The Chandra X-Ray Observatory, launched by the Space Shuttle Columbia in July 1999, has taken its place with the Hubble Space Telescope and Compton Gamma Ray Observatory in NASA's fleet of great space observatories. As the world's premier X-ray observatory, Chandra gives astronomers a powerful new tool to investigate black holes, exploding stars, and colliding galaxies in the hot regions of the universe. Chandra's uses four pairs of ultra smooth, high resolution mirrors and efficient X-ray detectors to produce images at least thirty times sharper then any previous X-ray telescope. Unfortunately, currently popular statistical analysis tools for such data typically involves Gaussian approximations (e.g., chi squared fitting) which are not justifiable for the high-resolution low-count data. In this paper, we employ modern Bayesian computational techniques (e.g., EM-type algorithms, the Gibbs sampler, and Metropolis-Hastings) to fit new hierarchical models that account for the Poisson nature of photon counts, background contamination, blurring of the image due to instrument response, photon absorption, and source features such as spectral energy lines. This application demonstrates the flexibility and power of modern Bayesian methodology and algorithms to handle highly hierarchical models that account for the complex structure in the collection of high-quality spectra. This is joint work with Vinay L. Kashyap and Aneta Siemiginowka.