The Peculiar X-ray Transient IGR 16358-4726The 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 - 4lwith the Chandra X-ray observatory at the 1.7 x 10(exp -l0) ergs/s sq cm flux level ( 2-10 keV) with a very high absorption column (N_H = 3.3 x 10(exp 23)/sq cm 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).