Abstract: There has been much recent interest in developing high spatial resolution vibrationally-selective microscopy techniques for imaging the chemical composition of biological and materials samples. However, several vibrations must be simultaneously excited for meaningful comparison between peaks in the spectrum. In this dissertation, the development of a multiplex coherent anti-Stokes Raman scattering (CARS) microscope featuring chirped femtosecond laser pulses to achieve high spectral resolution images of model samples is described. This technique is shown to achieve better than 10 cm-1 spectral resolution, ca. twenty times better than a transform-limited femtosecond pulse, and over a several hundred wavenumber multiplex bandwidth, utilizing a combination of chirped and unchirped femtosecond laser pulses. The spectral resolution of the technique is defined by the effective temporal overlap of the unchirped 100 femtosecond 'Stokes' pulse with a linearly chirped 'pump' pulse that was stretched by a pair of gratings to ca. 10 picoseconds in duration. Results for liquid hydrocarbon and solid-state polymer samples are presented. Images of polystyrene beads show contrast that arises from the C-H stretches of the aliphatic and aromatic functional groups of the beads, as seen in the point-specific spectra collected on and off the beads. Calculated femtosecond CARS spectra using chirped pump/probe and an unchirped Stokes pulses matched the experimental results for liquid methanol, confirming that the rate of the chirp of the pump/probe pulse governs the high spectral resolution. If the pump/probe pulses were not chirped, unresolved CARS spectra were observed both experimentally and theoretically. The calculations give insight into how the chirped pulses combine to achieve high spectral resolution by independently analyzing the real and imaginary contributions to the total CARS signal. Results from infrared absorption near-field microscopy experiments employing infrared synchrotron radiation, a carbon dioxide laser and lead-salt diode lasers are also presented. Preliminary results on both biological (lung cells) and materials (polystyrene beads) samples are described, but ultimately the flux of infrared light from both the synchrotron and lead-salt diodes were insufficient to achieve satisfactory images.