We present the results of a deep search for pulsations from the nearby isolated neutron star RX J1856.5-3754 using the 450 ks director's discretionary time Chandra observation completed on 2001 October 15. No pulsations were detected. We find a 99% confidence upper limit on the pulsed fraction of ~4.5% for worst-case sinusoidal pulsations with frequency ≲50 Hz and frequency derivatives -5 × 10 -10 Hz s -1 ≤ ≤ 0 Hz s -1 . The nondetection of pulsations is most likely due to an unfavorable viewing angle or emitting geometry. Such emitting geometries are much more likely to occur for more "compact" neutron stars, which show increased gravitational light-bending effects. In this case, the nondetection implies a radius-to-mass ratio for RX J1856.5-3754 of R / M ≲ 10 km M .
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