Branching fraction measurements from Fourier transform spectra in conjunction with published radiative lifetimes are used to determine transition probabilities for 263 lines of neutral chromium. These laboratory values are employed to derive a new photospheric abundance for the Sun: log $epsilon$(Cr I)$_{odot}$ = 5.64$pm$0.01 ($sigma = 0.07$). These Cr I solar abundances do not exhibit any trends with line strength nor with excitation energy and there were no obvious indications of departures from LTE. In addition, oscillator strengths for singly-ionized chromium recently reported by the FERRUM Project are used to determine: log $epsilon$(Cr II)$_{odot}$ = 5.77$pm$0.03 ($sigma = 0.13$). Transition probability data are also applied to the spectra of three stars: HD 75732 (metal-rich dwarf), HD 140283 (metal-poor subgiant), and CS 22892-052 (metal-poor giant). In all of the selected stars, Cr I is found to be underabundant with respect to Cr II. The possible causes for this abundance discrepancy and apparent ionization imbalance are discussed.
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