We describe the development of a CMOS read-out chip for an X-ray pixel array detector that accumulates into analog storage elements with time resolution typical of synchrotron bunch spacings. Each pixel contains multiple analog storage elements to allow capture of full-frame images at submicrosecond separation. Additionally, each storage element is re-addressable, which allows accumulation of signal from temporally distinct acquisition windows. Test results show the ability to slew and settle the equivalent of 650 8-keV x-rays (1.21 Me$^-$) in less than 100 ns. The detector RMS read-noise was measured to be 2350 e$^-$ and grows with the square-root of the number of accumulations with a coefficient of 415 e$^-$ (equivalent to 1.07 and 0.19 8-keV x-rays respectively). The saturation value for each storage element, in terms of 8 keV x-rays, was measured to exceed 1880 x-rays (6.42 Me$^-$). The complete detector is anticipated to contain around 400 x 200 pixels with pixel size near 150 $\mu$m times 150 $\mu$m. Possible experimental applications include study of material failures, transient phase transformations, and high-speed X-radiography.