Single frequency lasing from organic dye solutions on a monolithic poly(dimethylsiloxane) (PDMS) elastomer chip is demonstrated. The laser cavity consists of a single mode liquid core/PDMS cladding channel waveguide and a phase shifted 15th order distributed feedback (DFB) structure. A 1mM solution of Rhodamine 6G in a methanol and ethylene glycol mixture was used as the gain medium. Using 6 nanosecond 532nm Nd:YAG laser pulses as the pump light, we achieved threshold pump fluence of ~0.8mJ/cm(2) and single-mode operation at pump levels up to ten times the threshold. This microfabricated dye laser provides a compact and inexpensive coherent light source for microfluidics and integrated optics covering from near UV to near IR spectral region.