Using accurate positions from very deep radio observations to guide multi-object Keck spectroscopy, we have determined a substantially complete redshift distribution for very luminous, distant submillimeter(submm)-selected galaxies (SMGs). A sample of 73 redshifts for SMGs in 7 fields contains a surprisingly large number of `associations': systems of SMGs with Mpc-scale separations, and redshifts within 1200 km/s. This sample provides tentative evidence of strong clustering of SMGs at redshifts z~2-3 with a correlation length of about 6.9 +- 2.1 Mpc/h, using a simple pair-counting approach that is appropriate to the small, sparse SMG samples. This is somewhat greater than the well-determined correlation lengths for both z~3 optical-ultraviolet(UV) color-selected Lyman-break galaxies (LBGs) and z~2 QSOs. This could indicate that SMGs trace the densest large-scale structures in the high-redshift Universe, and that they may either be evolutionarily distinct from LBGs and QSOs, or subject to a more complex astrophysical bias.

7 pages; 3 figures; in press at ApJ (scheduled 20th August). Proof corrected copy