Google Chrome maximum cookie expiry date
I have just tried that on a 64bit OS with Chrome as a browser and Apache as a server, and it works flawlessly. It shows the cookie's expiration time to be somewhere in the year 2113.
dev-null-dweller is probably right: Any date beyond 03:14:07 UTC on Tuesday, 19 January 2038 will wrap around to some time close to 1900, thus forcing the cookie to immediately disappear (on 32bit platforms, that is).
Work around this by setting cookie expiration times to be no more than 10 years in the future, or so. This is already beyond the reasonably expectable lifetime of any electronic device, which will hold it, anyways.