We have studied the field dependence of the hyperfine splitting of holmium as a dilute substituent in a lamina of dysprosium prepared by molecular-beam epitaxy. The measurements were made by spin-echo NMR at temperatures below 2 K and in fields up to 8 T. In fields above 3 T we obtain sharp seven-line spectra which are characteristic of ¹⁶⁵Ho in fully polarized holmium ions in a ferromagnetically ordered host medium. The resolution is markedly superior to that obtained in bulk rare-earth alloys and has enabled us to resolve features hitherto unmeasurable. The form of the zero-field spectrum suggests that helimagnetic and ferromagnetic phases coexist in the zero-field-cooled material. Magnetization measurements support this interpretation.