In the present work, the approach of Furnstahl, Serot, and Tang (FST) is extended to the region of nonzero strangeness in application to single-particle states in single \Lambda-hypernuclei. To include  \Lambda 's, an additional contribution to their effective Lagrangian is systematically constructed within the framework of FST. The relativistic Hartree (Kohn--Sham) equations are solved numerically, and least-square fits to a series of experimental levels are performed at various levels of truncation in the extended Lagrangian. The ground-state properties of any  \Lambda-hypernuclei are then predicted. In addition, ground-state  \Lambda -particle--nucleon--hole splittings are calculated where appropriate, and the approach is calibrated against a calculation of the s_1/2-doublet splitting in the nucleus ³²₁₅{P}₁₇.

PACS numbers: 21.80.+a