  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 this
pulsar over 1.4~yr at several radio frequencies, from which we have derived
high precision rotational, astrometric, and orbital parameters. The upper limit
for the period derivative of the pulsar, dP/dt<4x10^-20, gives a characteristic
age of at least 1.6x10^10 yr, among the highest known. We find the orbit to be
precessing at a rate of 0.0111+-0.0002 yr^-1, which yields a total system mass
(pulsar plus companion) of 2.62+-0.07 M_solar according to general relativity.
Further analysis of the orbital parameters yields a firm upper limit of 1.75
M_solar on the pulsar mass and constrains the companion mass to the range 0.9
to 2.7 M_solar. These masses, together with the sizable orbital eccentricity
and other evidence, strongly suggest that the companion is a second neutron
star.
