We have designed and constructed a Hencken-type burner that produces a 38-mm-long linear laminar partially premixed co-flow diffusion flame. This burner was designed to produce a linear flame for studies of soot chemistry, combining the benefit of the conventional Hencken burner's laminar flames with the advantage of the slot burner's geometry for optical measurements requiring a long interaction distance. It is suitable for measurements using optical imaging diagnostics, line-of-sight optical techniques, or off-axis optical-scattering methods requiring either a long or short path length through the flame. This paper presents details of the design and operation of this new burner. We also provide characterization information for flames produced by this burner, including relative flow-field velocities obtained using hot-wire anemometry, temperatures along the centerline extracted using direct one-dimensional coherent Raman imaging, soot volume fractions along the centerline obtained using laser-induced incandescence and laser extinction, and transmission electron microscopy images of soot thermophoretically sampled from the flame.