We present a new economical microfluidic viscometer to measure the viscosity of biological fluids, using sample volumes of less than 200 μl. It is fabricated using a microwire-molding technique, making it easier and cheaper to produce than existing viscometers. The viscometer is based on laminar flow inside a polydimethylsiloxane microchip. The velocity of the sample flow inside the capillary was monitored with a camera, and the movement of the liquid column was determined by a Matlab video-processing program. The device was calibrated using deionized water, which is a Newtonian fluid, at 20 °C. The viscometer provides accurate measurements of viscosity for values as small as 0.69 mPa s. The viscosity of water at different temperatures was measured, showing more than 98% agreement with the values provided by the National Institute of Standards and Technology. Various samples including a series of glycerol solutions, phosphate-buffered saline, alcohol, and cell media were also tested, and the measured viscosities were compared with those from a traditional glass capillary viscometer. The results show good agreement between the two methods, with an average relative error of less than 1%. Furthermore, the viscosities of several cell suspensions were measured, showing a relative standard deviation of less than 1.5%. The microchip viscometer is economical and is shown to be accurate, which is very important for the simulation and control of lab-on-a-chip experiments.