It is possible, but it would not be very cost effective, and would require a lot of effort and expertise. To get a chip that would fit a G1's motherboard, you would probably have to take out the one in the MT3G(or possibly the HTC HERO) and solder that back into the G1. This would be pretty damn hard to do and expensive.
The ROM and RAM are combined onto one chip on the G1's motherboard, which means that if you put in a new chip, your system image, recovery image, and bootloader are all gone. So basically, even if you do manage to put in a new chip, you would essentially have a bricked device.
If you were really persistent, you could JTAG a new system image, recovery image, and bootloader onto the new chip, but a JTAG kit costs 40 bucks minimum.
It would be cheaper and less painful to just buy a new phone.