The miniaturization of synthesis, analysis and screening experiments is an important step towards more environmentally friendly chemistry, statistically significant biology and fast and cost-effective medicinal assays. The facile generation of arbitrary 3D channel structures in polymers is pivotal to these techniques. Here we present a method for printing microchannels directly into viscous curable polymer matrices by injecting a surfactant into the uncured material via a steel capillary attached to a 3D printer. We demonstrate this technique using polydimethylsiloxane (PDMS) one of the most widely used polymers for the fabrication of, e. g. microfluidic chips. We show that this technique which we term Suspended Liquid Subtractive Lithography (SLSL) is well suited for printing actuators, T-junctions and complex three dimensional structures. The formation of truly arbitrary channels in 3D could revolutionize the fabrication of miniaturized chips and will find broad application in biology, chemistry and medicine.