  We present the results of one year of pulse timing observations of PSR
J1740-5340, an eclipsing millisecond pulsar located in the globular cluster NGC
6397. We have obtained detailed orbital parameters and a precise position for
the pulsar. The radio pulsar signal shows frequent interactions with the
atmosphere of the companion, and suffers significant and strongly variable
delays and intensity variations over a wide range of orbital phases. These
characteristics and the binary parameters indicate that the companion may be a
bloated main-sequence star or the remnant (still filling its Roche lobe) of the
star that spun up the pulsar. In both cases, this would be the first binary
millisecond pulsar system with such a companion.
