It just so happens it was in the first book I picked up. It's a little bit longer than I would normally post but it is interesting, (Well i think it is.)
"Perhaps the most startling innovation was the borough's adoption of electric street lighting in 1881. This came about as the result of a squabble over the future terms of a new lighting contract by the Gas & Water Company, which shut off light for a month in September of that year. The problems caused by people blundering about the darkened streets of the town , and the complaints that resulted, led the corporation to take up the offer of Messers Hammond & Co to give a three week trial of the electric system. Eight arc lamps were installed in the centre of town, the dynamo driven by an 8hp engine located in Theatre yard. It proved a success and the corporation signed a contract for the town to be lit for another year by 22 arc lights and fifty Lane-Fox incandescent lamps. The scheme was in place by the summer of 1882, and generated interest throughout the country; a number of experts visited the town and went away impressed by what they saw. There has been some dispute over wether or not Chesterfield can fairly claim to the first town lit by electricity. Godalming, it's main rival, also adopted electric lighting in 1881 a few days earlier using a water powered system, but while the Chesterfield scheme succeeded Godalming's system proved a short lived failure. So, Chesterfield can certainly claim to be the first town successfully lit by electricity. Unfortunately the honemoon period with Hammond & Co did not last long. The company was not making an economic return from lighting the streets and wanted to run further wires for the more profitable lighting of shops and houses in the town. The corporation drew the line at this and the agreement lapsed. The Gas & Water Company returned with more favourable terms and Chesterfield reverted to gaslight in 1884. It was a sad postscript to what had been a daring experiment." from History & Guide to Chesterfield by Geoff Sadler.