This work presents the development and analysis of a system that combines the concepts of light field microscopy and particle image velocimetry (PIV) to measure three-dimensional velocities within a microvolume. Rectanglar microchannels were fabricated with dimensions on the order of 350-950 micrometers using a photolithographic process and polydimethylsiloxane (PDMS). The flow was seeded with fluorescent particles and pumped through microchannels at Reynolds numbers ranging from 0.016 to 0.028. Flow at Reynolds numbers in the range of 0.02 to 0.03 was seeded with fluorescent particles and pumped through microchannels. A light field microscope with a lateral resolution of 6.25 micrometers and an axial resolution of 15.5 micrometers was designed and built based on the concepts described by Levoy et al. Light field images were captured continuously at a frame rate of 3.9 frames per second using a Canon 5D Mark II DSLR camera. Each image was post processed to render a stack of two-dimensional images. The focal stacks were further post processed using various methods including bandpass filtering, 3D deconvolution, and intensity-based thresholding, to remove effects of diffraction and blurring. Subsequently, a multi-pass, three-dimensional PIV algorithm was used to measure channel velocities. Results from PIV analysis were compared with an analytical solution for fully-developed cases, and with CFD simulations for developing flows. Relative errors for fully-developed flow measurements, within the light field microscope refocusing range, were approximately 5% or less. Overall, the main limitations are the reduction in lateral resolution, and the somewhat low axial resolution. Advantages include the relatively low cost, ease of incorporation into existing micro-PIV systems, simple self-calibration process, and potential for resolving instantaneous three-dimensional velocities in a microvolume.