Surveyor Program landers (1-7) made robotic soft-landing on the lunar surface. The major difference between Surveyor landers and Chang'e 3 is that they didn't orbit the Moon, but were put on a ballistic trajectory and the autopilot computer did the rest. NASA page on Surveyor 1 puts the soft-landing procedure like this:
For the landing sequence, an altitude marking radar initiated the
firing of the main retrorocket for primary braking. After firing was
complete, the retrorocket and radar were jettisoned and the doppler
and altimeter radars were activated. These provided information to the
autopilot which controlled the vernier propulsion system to touchdown.
To my knowledge, all other Surveyor landers used the same landing procedure. Chang'e will however attempt landing from a low-inclination elliptical lunar orbit with perilune (lunar perigee) at only 15 kilometers. Emily Lakdawalla describes Chang'e 3 landing phase in The Planetary Society blog post like this:
The descent engine will be ignited at 15 kilometers to decelerate,
above 2 kilometers it'll have pointed its main engine downward, below
2 kilometers it'll be slowly descending. At 100 meters the payload
will be hovering without receiving control from Beijing. It'll utilize
its camera and computer to identify the surface, and automatically
select a plain to land on. At 4 meters the descent engine will turn
off, and the payload will land with a free fall.
Robotic landing computer of Surveyor landers was programmed to target free-fall soft landing from about 3.4 meters (11 feet), so this is also fairly similar to what Chang'e 3 carrying Yutu lunar rover will attempt. The major difference being the angle of the approach vector, enabling the lander to autonomously decide on the most suitable landing site. Surveyor landers didn't utilize anything like this (technology in 60's wasn't really capable of autonomous decisions like that, and since they landed from a ballistic trajectory, there wouldn't be much leeway for maneuvering anyway).
About the communications delay though, I don't think the distance to the Moon is the reason they didn't decide for a remote-controlled landing. The majority of the delay would come from the communications network (CDSN) relaying communications one station to another, and also from the controllers themselves to react to fast changing situation fast enough, while keeping their action synchronised with whatever communications delay would there be. This would be similarly hard than conducting an orchestra, without having any previous experience with any of its musicians. And since humans aren't infallible either, they must have decided it's simply easier to leave it to the onboard computer. One more thing about it is that if they attempted a remote controlled descent, it would complicate matters anyway, since the vehicle would have to keep its communications antenna pointed towards the Earth at all times, while changing orientation. This would also constantly shift vehicle's center of mass. So accounting for all these complications, autonomous landing just sounds a lot simpler.
Additionally, since you asked about remote operated hardware at a distance to the Moon, it is not impossible and has been done before. Some Apollo missions (the ones with lunar rovers) left TV cameras on the surface to transmit live pictures of ascent module liftoffs, and cameras of some of these Apollo missions were remote operated from Earth to provide a better view of the ascent. This required great skill from the camera operator, because he had to issue commands to the camera in advance and with communications delay in mind, while also anticipating the time when the ascent module will actually fire its ascent engines. During the Apollo 17 mission, this succeeded perfectly, as can be seen in this video on YouTube (notice the zoom-out first, then slow tilt of the camera to keep the module inside the camera's frame).
