The creation of geometrically complex fluidic devices is a subject of broad fundamental and technological interest. Here, we demonstrate the fabrication of three-dimensional (3D) microvascular networks through direct-write assembly of a fugitive organic ink. This approach yields a pervasive network of smooth cylindrical channels (approximately 10-300 microm) with defined connectivity. Square-spiral towers, isolated within this vascular network, promote fluid mixing through chaotic advection. These vertical towers give rise to dramatic improvements in mixing relative to simple straight (1D) and square-wave (2D) channels while significantly reducing the device planar footprint. We envisage that 3D microvascular networks will provide an enabling platform for a wide array of fluidic-based applications.