The new transient IGR 16358 - 4726 was discovered on 2003 March 19 with INTEGRAL . We detected the source serendipitously during our 2003 March 24 observation of SGR 1627 - 41 with the Chandra X-ray observatory at the 1.7 \times 10 ^ { -10 } ergs s ^ { -1 } cm ^ { -2 } flux level ( 2 - 10 keV ) with a very high absorption column ( N _ { H } = 3.3 \times 10 ^ { 23 } cm ^ { -2 } ) and a hard power law spectrum of index 0.5 ( 1 ) . We discovered a very strong flux modulation with a period of 5880 ( 50 ) s and peak-to-peak pulse fraction of 70 ( 6 ) % ( 2 - 10 keV ) , clearly visible in the x-ray data . The nature of IGR 16358 - 4726 remains unresolved . The only neutron star systems known with similar spin periods are low luminosity persistent wind-fed pulsars ; if this is a spin period , this transient is a new kind of object . If this is an orbital period , then the system could be a compact Low Mass X-ray Binary ( LMXB ) .