We have developed a multi-sample micro-slit rheometer (MMR) which is capable of measurements over a broad range of temperatures, viscosities and shear rates. The instrument is mechanically simple as the flow is generated by external gas pressure and the shear rate is measured through optical tracking of the flow front. In the current implementation, the required volume of each sample is approximately 20 mu L and we measure four samples simultaneously. We demonstrate the performance of the MMR by measurement of the flow curves (viscosity versus shear rate) of three representative polymers: A polydimethylsiloxane melt, a polyisobutylene solution, and a polystyrene melt. We adapt standard data correction methods to account for shear-thinning and entry/flow-front effects. We report a high level of accuracy and precision. This instrument will be particularly useful in cases of multiple samples, limited material quantity, and when optical access is useful.