Polydimethylsiloxane is a translucent and biologically inert silicone material used in sealants, biomedical implants and microscale lab-on-a-chip devices. Furthermore, in membrane technology, polydimethylsiloxane represents a material for separation barriers as it has high permeabilities for various gases. The facile handling of two component formulations with a silicone base material, a catalyst and a small molecular weight crosslinker makes it widely applicable for soft-lithographic replication of two-dimensional device geometries, such as microfluidic chips or micro-contact stamps. Here, we develop a new technique to directly print polydimethylsiloxane in a rapid prototyping device, circumventing the need for masks or sacrificial mold production. We create a three-dimensional polydimethylsiloxane membrane for gas-liquid-contacting based on a Schwarz-P triple-periodic minimal-surface, which is inaccessible with common machining techniques. Direct 3D-printing of polydimethylsiloxane enables rapid production of novel chip geometries for a manifold of lab-on-a-chip applications.