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Re:CentOS 7 released on x86_64 by cwyers on Monday July 07, 2014 @03:55PM (#8000995)
It looks like the listed minimum for RHEL 6 was 1gb[1]. I don't think 128 was officially supported even then, so if you're happy with how it works now, you may still be happy with 7.

1) http://www.slac.stanford.edu/comp/unix/linux/install_RHEL6.h...

Re:CentOS 7 released on x86_64 by netcraft on Monday July 07, 2014 @04:00PM (#8001036)
The installer requires 406mb of ram to work: http://wiki.centos.org/Manuals/ReleaseNotes/CentOS7#head-281...
Re:CentOS 7 released on x86_64 by 3h8d on Monday July 07, 2014 @08:06PM (#8002330)
Would it be possible to assign swap to a removable media device and then bootstrap the installer to run in that environment on a device with 128mb?
Re:CentOS 7 released on x86_64 by noselasd on Monday July 07, 2014 @08:29PM (#8002411)
Probably. You'll have to hack the install procedure to enable swapping before it's being run though.

If you're serious about trying this, the fastest path is to install CentOS in a VM on a suitable machine that isn't going to spend a day in the installer swapping like crazy, and copy the image to a physical drive which you eventually stuff into the ancient low memory box.