In the body, capillary beds fulfill the metabolic needs of cells by acting as the sites of diffusive transport for vital gasses and nutrients. In artificial tissues, replicating the scale and complexity of these capillary vessels has proved challenging, especially in a three-dimensional context. In order to better develop thick artificial tissues, it will be necessary to recreate both the form and function of capillaries. Here we demonstrate a top-down method of patterning hydrogels using sacrificial templates formed from thermoresponsive microfibers whose size and architecture approach those of natural capillaries. Within the resulting microchannels, we cultured endothelial monolayers that remain viable for over three weeks and exhibited functional barrier properties. Additionally, we cultured endothelialized microchannels within hydrogels containing fibroblasts and characterized the viability of the co-cultures to demonstrate this approach's potential to when applied to cell-laden hydrogels. This method represents a step forward in the evolution of artificial tissues and a path towards producing viable capillary-scale microvasculature for engineered organs.