We grew thin films of a heavy fermion chiral magnet YbNi\(_3\)Al\(_9\) by using molecular beam epitaxy. They were grown on \(c\)-plane sapphire substrates under ultra-high vacuum while maintaining a deposition rate at a stoichiometric ratio among Yb, Ni, and Al. The resulting thin films contain epitaxial grains with a \(c\) axis parallel to the substrate surface: The YbNi\(_3\)Al\(_9\) \(c\) axis is parallel to the sapphire \(b\) or \(a\) axis. The temperature dependence of the resistivity exhibits a typical feature of a dense Kondo system with a broad shoulder structure at \(\sim\)40\,K, as well as a kink as a signature of the chiral helimagnetic ordering at 3.6\,K. These features are consistent with those previously observed in bulk samples. The shift in the kink associated with the field-induced phase transition is found in the magnetoresistance curves under a magnetic field applied in the direction perpendicular to the \(c\)-axis. The magnetic phase diagram well reproduces that for the bulk crystals, implying that the chiral soliton lattice phase arises under magnetic fields, even in thin films.