High‐quality epitaxial Y1B2Cu3Oxthin films (Tc,o≥ (R18) 90 K,jc(77 K)≥ (R18)3 ×106A/cm2) wereinsitugrown on MgO by KrF excimer laser ablation. The combination ofinsituresistance measurements, x‐ray diffraction experiments,Tcmeasurements, scanning electron microscopy and scanning tunneling microscopy gives clear indications for an island growth on these substrates and shows growth steps and spirals at the film surface.