PSR J0737-3039, 2000 ly away. There are neutron stars in binary systems, and in some cases the companion is also a neutron star but as far as I know this is the only known double pulsar system, found in 2004.

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Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself, and you are the easiest person to fool.
-- Richard Feynman