Chip Count:
1) Z80
2) 62256 SRAM
3) 28C256 EEPROM
4) 74LS32 (memory access decoder)
5) 74LS04 (RAM/ROM decoder)
6) 74LS138 (I/O decoder)
7) 8250 UART (serial port)
8) MAX232 (TTL to RS232 voltage converter)
Looks good, though I may have missed out on one. I included the 8250 UART so you can get a serial port, you want to be able to see some output.
This is as simple as a computer can get, trying to get it under 8 chips and still maintain functionality is tricky, unless you want a traffic light controller.
There is 64K of address space on the Z80, in this basic configuration there is 32K ROM and 32K RAM which fills it. There is still room for I/O devices on the 256 byte port address space. Notice on the Z80 pinouts how there are MEMRQ and IORQ lines, these are for Memory Request and I/O Request, which means that the I/O ports are addressed separately from memory.