toto guinevere running constantly, help!

We just had a toto guinevere installed. It trickles water constantly out of the tank, then fills a little, and screeches as the water shuts off. I jiggled the flapper ( I am not a plumber..Hahaha) That sometimes helps, then it will start up again. This is really annoying, especially when it happens repeatedly, at night. I am tempted to turn off the water, but then what's the point of having a brand new toilet??? It does seem to be leaking through the flapper, or somewhere else (it's a one piece toilet).
I asked the plumber who installed the toilet about it... His answer "these toilets do better if they are used" Hey, we ARE using it! Does he mean the flappers get dried out while the toilets are sitting in the warehouse??? what's with this. He is telling me that I will have to pay him extra to fix it. I am tempted to fix it myself, if I know what to do.. Please, gentlemen, and ladies, what should I do???
Many thanks to all and to Terry for the forum

If the plumber supplied the toilet (you bought it from him), he should make it work, otherwise, you'd pay for a return call. Several things: the chain could have too much slack, and it is getting caught underneath the flapper valve. Or, it could be too short, and is holding it up (or has a kink in it, not letting the flapper seat). Or, there's a defect on the seat where the flapper sits (or just some crud stuck there - it should be smooth and even). Or, the flapper is bad (Toto will send you a new one if you call). A close visual inspection and maybe a feel around the valve seat should identify the problem.

It may be the flapper, or it may be the seal under the flush valve. The flush valve is held in place by two blocks attached with screws. When the flapper is lifted up, you can see them. Loosen them up, but don't remove them. Swivel the blocks inward and lift out the flush valve. You may need to hit the inside of the tank with some emory cloth if there are any spots or rough edges that prevent the black rubber o-ring from sealing.