In the first six months of COVID-19 vaccine distribution, over 90% of all doses were given to residents of high and upper middle income nations. Less than 30% of Africans were vaccinated with at least one shot even 18 months after vaccine development. This has led to an explosion of scholarly and policy interest on vaccine hesitancy and ways to overcome it. We argue instead that the limiting factor for many rural Africans is lack of access, and implemented an intervention designed to overcome the logistical challenges of last-mile delivery. The cluster randomized controlled trial in 150 remote rural communities shows that simply bringing vaccines to villages using mobile vaccination teams increases the community vaccination rate by 20 percentage points within just 48-72 hours. Moreover, auxiliary populations showed up at our temporary clinic to get vaccinated, which lowers the cost of this intervention to US$ 32 per person vaccinated. This is more cost-effective than most vaccination strategies investigated via trials.