The Nuclear Spectroscopic Telescope Array (NuSTAR), scheduled for launch in 2011, is a NASA Small Explorer mission that will improve the current sensitivity for detection of faint astrophysical sources in the 6-80 keV band by two orders of magnitude. NuSTAR achieves high sensitivity by utilizing a hard X-ray focusing system. We have developed Cadmium Zinc Telluride (CdZnTe) pixel detectors optimized for good energy for the NuSTAR focal plane. Each of NuSTAR's two focal planes is comprised of hybrid detectors that consist of a CdZnTe pixel sensor with the anode contacts directly attached to corresponding readout circuits integrated on a custom low-noise VLSI chip. Each hybrid is 20.5 x 20.5 x 2.0 mm in size with the anode divided into 32 x 32 array of pixels at 0.6048 mm. In this paper we describe the hybrid sensor architecture, and present preliminary results from the characterization of detectors fabricated for the NuSTAR focal plane Engineering Test Unit (ETU). We achieve excellent electronic readout noise with an average of 250 eV FWHM, and energy resolution between 0.9 and 1.6 keV FWHM at 86.5 keV, depending on position in the sensor and improving at lower energies. In order to achieve the best spectral resolution we need to make pixeldependent corrections for events with charge split among multiple pixels, and in addition we make spectral corrections based on depth of the gamma-ray interaction.