Spatial models of vascularized tissues are widely used in computational physiology, to study for example, tumour growth, angiogenesis, osteogenesis, coronary perfusion and oxygen delivery. Composition of such models is time-consuming, with many researchers writing custom software for this purpose. Recent advances in imaging have produced detailed three-dimensional (3D) datasets of vascularized tissues at the scale of individual cells. To fully exploit such data there is an increasing need for software that allows user-friendly composition of efficient, 3D models of vascularized tissue growth, and comparison of predictions with in vivo or in vitro experiments and other models. Microvessel Chaste is a new open-source library for building spatial models of vascularized tissue growth. It can be used to simulate vessel growth and adaptation in response to mechanical and chemical stimuli, intra- and extra-vascular transport of nutrient, growth factor and drugs, and cell proliferation in complex 3D geometries. The library provides a comprehensive Python interface to solvers implemented in C++, allowing user-friendly model composition, and integration with experimental data. Such integration is facilitated by interoperability with a growing collection of scientific Python software for image processing, statistical analysis, model annotation and visualization. The library is available under an open-source Berkeley Software Distribution (BSD) licence at https://jmsgrogan.github.io/MicrovesselChaste. This article links to two reproducible example problems, showing how the library can be used to model tumour growth and angiogenesis with realistic vessel networks.