Using density functional theory the ground state structural, electronic, and magnetic properties of monatomic lithium and sodium chains with low average density are investigated. A metallic, zigzag ground state structure is predicted but, most interestingly, stable equilibria for chains under tension are predicted to be {\it ferromagnetic}, which can be traced to exchange effects arising from occupation of the second subband as a function of the interatomic distance. ; Comment: Revised version; 4 pages, 4 figures; to appear in International Journal of Quantum Chemistry (2003)