1963 Colt 45 John Paciorek (brother of ex-Nats announcer Tom "Wimpy" Paciorek) 3 for 3 lifetime 1.000 BA
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The only Nationals player I could find with an 1.000 lifetime BA is Travis Hughes!
The righthanded pitcher went 1 for 1 in 2006 for Washington.
Only picture I could find was in a BoSox hat.