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High-energy and nuclear physics experiments need tracking devices with increasing spatial precision and readout speed in the face of ever-higher track densities and increased radiation environments. The new generation of hybrid pixel detectors (arrays of silicon diodes bump-bonded to arrays of front-end electronic cells) is the state-of-the-art technology able to meet these challenges. We report on irradiation studies performed on BTeV pixel readout chip prototypes exposed to a 200-MeV proton beam at the Indiana University Cyclotron Facility. A prototype pixel readout chip (preFPIX2) has been developed at Fermilab for collider experiments and implemented in standard 0.25-μm CMOS technology following radiation-tolerant design rules. The chip contains a variety of functional blocks (analog front ends, registers, state machines, and digital-to-analog converters). The tests confirm the radiation tolerance to proton total dose up to 87 Mrad of all of these circuits. In addition, nondestructive radiation-induced single-event upsets have been observed in on-chip static registers, and the single-bit upset cross-section has been extensively measured.