The Galileo High Accuracy Service (HAS) is a free of charge Global Navigation Satellite System (GNSS) augmentation service provided by the European Union. It is designed to enable real-time Precise Point Positioning (PPP) with a target accuracy (at the 95% confidence level) of 20 cm and 40 cm in the horizontal and vertical components, respectively, to be achieved within 300 s. The performance of the service has been confirmed with geodetic-grade receivers. However, mass market applications require low-cost GNSS receivers connected to low-cost antennae. This paper focuses on the performance of the real-time static and kinematic positioning achieved with Galileo HAS and low-cost GNSS receivers. The study is limited to GPS+Galileo dual-frequency positioning, thus exploiting the full potential of Galileo HAS SL1. We demonstrate that the target accuracy of Galileo HAS SL1 is reached with both geodetic-grade and low-cost receivers in dual-frequency static and kinematic applications in open-sky conditions. Precision of a few centimeters is reached for static positioning, while kinematic positioning results in subdecimeter precision. Vertical accuracy is limited by missing phase center offset models for low-cost antennas. In general, the performance of low-cost hardware using Galileo HAS for real-time PPP is comparable to that of geodetic-grade hardware. Therefore, combining low-cost GNSS receivers with Galileo HAS is feasible and justified.