PSR J1518+4904 is a recently discovered 40.9 ms pulsar in an 8.6 day,
moderately eccentric orbit. We have measured pulse arrival times for t
his pulsar over 1.4 yr at several radio frequencies, from which we hav
e derived high-precision rotational, astrometric, and orbital paramete
rs. The upper limit for the period derivative of the pulsar, P < 4 x 1
0(-20), gives a characteristic age of at least 1.6 x 10(10) yr, which
is among the highest known. We find the orbit to be precessing at a ra
te of 0 degrees.0111 +/- 0 degrees.0002 yr(-1), which yields a total s
ystem mass (pulsar plus companion) of 2.62 +/- 0.07 M(.) according to
general relativity. Further analysis of the orbital parameters yields
a firm upper limit of 1.75 M(.) on the pulsar mass and constrains the
companion mass to the range 0.9-2.7 M(.). These masses, together with
the sizable orbital eccentricity and other evidence, strongly suggest
that the companion is a second neutron star.