This paper presents a stochastic approach to single-phase and three-phase EV charge hosting capacity for distribution networks. The method includes the two types of uncertainties, aleatory and epistemic, and is developed from an equivalent method that was applied to solar PV hosting capacity estimation. The method is applied to two existing low-voltage networks in Northern Sweden, with six and 83 customers. The lowest background voltage and highest consumption per customer are obtained from measurements. It is shown that both have a big impact on the hosting capacity. The hosting capacity also depends strongly on the charging size, within the range of charging size expected in the near future. The large range in hosting capacity found from this study—between 0% and 100% of customers can simultaneously charge their EV car—means that such hosting capacity studies are needed for each individual distribution network. The highest hosting capacity for the illustrative distribution networks was obtained for the 3.7 kW single-phase and 11 kW three-phase EV charging power.