A term specific to land surveying. A chain is used to measure distances. Historically, it really was a chain, but in more modern times, it is a thin steel tape, typically 100 or 200 feet long.
Chainmen come in two varieties: head and rear. The head chainman holds the "zero" end of the chain (which has tenths and hundredths of a foot etched into it after the zero mark); also known as the "small end".
The job of the rear chainman is the worst. The chain must be held over the point (transit point, benchmark, whatever); usually with a plumb bob to adjust for differences in altitude (the chain must be held horizontally - there's no use measuring if you're measuring up or down a slope). The rear chainman holds the chain with the nearest foot over the point. The head chainman pulls the chain taught (pulling very hard, making life hard for the rear chainman) and lines it up next to a plumb bob dropped over the point to be measured. The rear chainman calls off the feet and the head chainman then calls off the tenths and hundredths of a foot left over.
In modern circumstances, of course, no one chains distances anymore. Electronic distance meters that use lasers or microwaves can measure distances to within one part per million.
See: land surveying.