The magnetism and the morphology of one-dimensional Fe stripes on a Cu(111) vicinal surface with perpendicular magnetization are investigated. Scanning tunneling microscopy shows that the Fe stripes have nanometer width and are aligned in parallel along the [011] direction. From the magnetization curves it is inferred that the stripes exhibit a ferromagnetic behavior well below the nominal thickness of one monolayer. In contrast to two-dimensional films, the magnetization of the stripes is not only temperature but also time dependent. The dynamics of the stripes have been described by a micromagnetic Ising model with Glauber dynamics, yielding an effective anisotropy constant K₁ of 0.65±0.15 M J/m³