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There are two reasons for this problem. Either the iPhoto application is corrupted or it is the iPhoto Library that has corrupted. We can rebuild your iPhoto Library and see if that works or not.
Close iPhoto if it is open. Hold down the Command and Option keys on the keyboard and open iPhoto. Keep the keys held down until you are prompted to rebuild the library. A dialog will appear with rebuild options. Select all the options/checkboxes Click Rebuild. This may take a few minutes to complete.
After rebuilding, iPhoto will open.
If it is still quitting after rebuilding, then we have to rebuild the iPhoto application using a third party application named iPhoto Library Manager. Download and install it from here (use the trial version) : http://www.fatcatsoftware.com/iplm/
Open iPhoto Library Manager. Select your iPhoto Library, click on Library menu in the top and select Rebuild Library. This will verify the library. Then click the Rebuild button on the right side.
After rebuilding, open iPhoto.
Please let me know if that didn't work, so we can continue troubleshooting.