The human immunodeficiency virus type 1 (HIV-1) envelope (Env) spike, comprising three gp120 and three gp41 subunits, is a conformational machine that facilitates HIV-1 entry by rearranging from a mature unliganded state, through receptor-bound intermediates, to a post-fusion state. As the sole viral antigen on the HIV-1 virion surface, Env is both the target of neutralizing antibodies and a focus of vaccine efforts. Here we report the structure at 3.5 Å resolution for an HIV-1 Env trimer captured in a mature closed state by antibodies PGT122 and 35O22. This structure reveals the pre-fusion conformation of gp41, indicates rearrangements needed for fusion activation, and defines parameters of immune evasion and immune recognition. Pre-fusion gp41 encircles amino- and carboxy-terminal strands of gp120 with four helices that form a membrane-proximal collar, fastened by insertion of a fusion peptide-proximal methionine into a gp41-tryptophan clasp. Spike rearrangements required for entry involve opening the clasp and expelling the termini. N-linked glycosylation and sequence-variable regions cover the pre-fusion closed spike; we used chronic cohorts to map the prevalence and location of effective HIV-1-neutralizing responses, which were distinguished by their recognition of N-linked glycan and tolerance for epitope-sequence variation.