Raman spectroscopy is a powerful optical and non-destructive technique and a well-known method for analysis purposes, especially to determine the molecular fingerprint of substances. Traditionally, such analyses are done in a specialized lab, with considerable requirements in terms of equipment, time and manual sampling of substances of interest. In this paper we take a step from bulky Raman spectroscopy laboratory analyses towards lab-on-chip (LOC) analyses. We present an optofluidic lab-on-chip for confocal Raman spectroscopy, which can be used for the analysis of liquids. The confocal detection suppresses the unwanted background from the polymer material out of which the chip is fabricated. We design the free-form optical reflector using non-sequential ray-tracing combined with a mathematical code to simulate the Raman scattering behavior of the substance under test. We prototype the device in Polymethyl methacrylate (PMMA) by means of ultraprecision diamond tooling. In a proof-of-concept demonstration, we first show the confocal behavior of our Raman lab-on-chip system by measuring the Raman spectrum of ethanol. In a next step, we compare the Raman spectra measured in our lab-on-chip with spectra measured with a commercial Raman spectrometer. Finally, to calibrate the system we perform Raman measurements on urea solutions with different concentrations. We achieve a detection limit that corresponds to a noise equivalent concentration of 20mM. Apart from strongly reducing the background perturbations, our confocal Raman spectroscopy system has other advantages as well. The reflector design is robust from a mechanical point of view and has the potential for mass-manufacturing using hot embossing or injection molding.