With his first and second-choice keepers Petr Cech and David Ospina both out through injury, Wenger is forced to name Emiliano Martinez between the sticks in what is his first Premier League appearance since December 2014.
Matt Macey, a 22-year-old who is yet to make a senior appearance for the Gunners, is named as Martinez's deputy on the bench.
There is one change in defence from the 2-2 draw with Manchester City on Sunday as Gabriel Paulista is deployed as a centre-back alongside Shkodran Mustafi after Laurent Koscielny was ruled out with an Achilles injury. Hector Bellerin continues at right-back, with Nacho Monreal operating on the left.
Aaron Cresswell misses out on the trip across the capital and is replaced at left-back by the returning Arthur Masuaku, while Sam Byram, Jose Fonte and James Collins retain their places ahead of Darren Randolph between the sticks.
Elsewhere, Diafra Sakho is named among the substitutes after four months out with a back injury.
Arsenal: Martinez; Bellerin, Mustafi, Gabriel, Monreal; Elneny, Xhaka; Walcott, Ozil, Alexis; Welbeck
Subs: Macey, Mertesacker, Gibbs, Ramsey, Oxlade-Chamberlain, Iwobi, Giroud
West Ham United: Randolph; Byram, Collins, Fonte, Masuaku; Kouyate, Noble, Antonio, Lanzini, Ayew; Carroll
Subs: Adrian, Nordtveit, Fernandes, Feghouli, Snodgrass, Sakho, Calleri
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