Resistors to make an 74hcxx IC behave like a 74hctxx IC
You may be able to add pull-up resistors to the AT28C256 outputs to get its High output voltage closer to Vcc, and acceptable to the 74HC part.

The actual switching threshold for the 74HC parts may be close to 2.5 volts, and the AT28C256 output High is probably well above 2.4 volts, so your circuit may work fine, with no modification - but I wouldn't trust it in a production situation.