A systematic analysis of the X-ray emission from the nearby ultraluminous infrared galaxy Mrk 273 was carried out by combining new 200 ksec Chandra data with archived 44 ksec data. The active galactic nucleus (AGN) associated with the Southwest nucleus is confirmed by the new data, and a secondary hard X-ray (4-8 keV) point source is detected, coincident with the Northeast nucleus at a projected distance of 0.75 kpc from the Southwest nucleus. The hard X-ray spectrum of the Northeast nucleus is consistent with a heavily absorbed AGN, making Mrk 273 another example of a dual AGN in a nearby galaxy merger. Significant 1-3 keV emission is found along the ionization cones and outflowing gas detected in a previous study. The data also map the giant X-ray nebula south of the host galaxy with unprecedented detail. This nebula extends on a scale of $sim$ 40 kpc $times$ 40 kpc, and is not closely related to the well-known tidal tail seen in the optical. The X-ray emission of the nebula is best described by a single-temperature gas model, with a temperature of $sim$ 7 million K and a super-solar $alpha$/Fe ratio. Further analysis suggests that the southern nebula has most likely been heated and enriched by multiple galactic outflows generated by the AGN and/or circumnuclear starburst in the past, on a time scale of $lesssim$0.1 Gyr, similar to the merger event itself.