The endosomal sorting complexes required for transport (ESCRTs) facilitate endosomal sorting of ubiquitinated cargo, MVB biogenesis, late stages of cytokinesis, and retroviral budding. Here we show that ubiquitin associated protein 1 (UBAP1), a subunit of human ESCRT-I, coassembles in a stable 1:1:1:1 complex with Vps23/TSG101, VPS28, and VPS37. The X-ray crystal structure of the C-terminal region of UBAP1 reveals a domain that we describe as a solenoid of overlapping UBAs (SOUBA). NMR analysis shows that each of the three rigidly arranged overlapping UBAs making up the SOUBA interact with ubiquitin. We demonstrate that UBAP1-containing ESCRT-I is essential for degradation of antiviral cell-surface proteins, such as tetherin (BST-2/CD317), by viral countermeasures, namely, the HIV-1 accessory protein Vpu and the Kaposi sarcoma-associated herpesvirus (KSHV) ubiquitin ligase K5.