Abstract: A multiple-chain trenching machine comprises a prime mover with a trenching head assembly operably connected thereto. The trenching head may be raised, lowered, and/or pivoted relative to the prime mover, and comprises: a) a frame operably connected to the prime mover at a proximal end; b) one or more pairs of proximal and distal primary sprockets mounted on the frame; c) a primary endless-chain digging assembly engaged with and circulating around each pair of primary sprockets; d) one or more pairs of proximal and distal secondary sprockets mounted on the frame; e) a secondary endless-chain digging assembly engaged with and circulating around each pair of secondary sprockets. The primary chains are substantially wider than the secondary chains, and the diameters and positions of the sprockets may be such that each of the secondary chains cuts more deeply into the ground formation than the primary chains, thereby producing a narrow relief slot corresponding to each secondary chain.