A rose assembly for a lockset configured to conceal and protect at least portions of a chassis that are positioned in a through-hole of an entryway device. The rose assembly can include at least a rose base and a rose plate. The rose plate can be assembled to the rose base at one of a plurality of orientations so that the rose assembly has an asymmetrical configuration. The rose assembly can include an indexing system to control the orientations at which the rose plate can be selectively secured to the rose base. The indexing system can include first and second male members and a plurality of female members, the first male member being sized to be matingly received in some, but not all, of the plurality of female members. The rose plate can be secured to the rose base by plate fasteners, magnets and/or double-sided tape.