How sex is determined in insects is diverse and dynamic, and includes male heterogamety, female heterogamety, and haplodiploidy. In many insect lineages, sex determination is either completely unknown or poorly studied. We studied sex determination in Psocodea-a species-rich order of insects that includes parasitic lice, barklice, and booklice. We focus on a recently discovered species of Liposcelis booklice (Psocodea: Troctomorpha), which are among the closest free-living relatives of parasitic lice. Using genetic, genomic, and immunohistochemical approaches, we show that this group exhibits paternal genome elimination (PGE), an unusual mode of sex determination that involves genomic imprinting. Controlled crosses, following a genetic marker over multiple generations, demonstrated that males only transmit to offspring genes they inherited from their mother. Immunofluorescence microscopy revealed densely packed chromocenters associated with H3K9me3-a conserved marker for heterochromatin-in males, but not in females, suggesting silencing of chromosomes in males. Genome assembly and comparison of read coverage in male and female libraries showed no evidence for differentiated sex chromosomes. We also found that females produce more sons early in life, consistent with facultative sex allocation. It is likely that PGE is widespread in Psocodea, including human lice. This order represents a promising model for studying this enigmatic mode of sex determination.