By measuring the fringe visibility in a Young's double pinhole experiment, we demonstrate that quasi-phase-matched high-harmonic generation produces beams with very high spatial coherence at wavelengths around 13 nm. To our knowledge these are the highest spatial coherence values ever measured at such short wavelengths from any source without spatial filtering. This results in a practical, small-scale, coherent, extreme-ultraviolet source that is useful for applications in metrology, imaging, and microscopy.