Dislocations represent an important and ubiquitous class of topological defect found at the surfaces of metal oxide materials. They are thought to influence processes as diverse as crystal growth, corrosion, charge trapping, luminescence, molecular adsorption, and catalytic activity; however, their electronic and chemical properties remain poorly understood. Here, through a detailed first-principles investigation into the properties of a surface-terminated screw dislocation in MgO we provide atomistic insight into these issues. We show that surface dislocations can exhibit intriguing electron trapping properties which are important for understanding the chemical and electronic characteristics of oxide surfaces. The results presented in this article taken together with recent experimental reports show that surface dislocations can be equally as important as more commonly considered surface defects, such as steps, kinks, and vacancies, but are now just beginning to be understood.