EEPROM IC

Besides the I2C eeproms that G_M mentioned, there are also SPI eeproms of the same
size, 128KBytes,

In addition, there are SPI Flash rom chips much larger, up to 16MBits and more, but I believe
all of these operate at 3.3V only.

http://www.digikey.com/product-search/en/integrated-circuits-ics/memory/2556980?k=flash%20spi