Why bother with running an electric motor, to drive a hydraulic pump, to run a heavy, expensive chainsaw, when you can plug one into a standard electrical outlet?
I have 3 electric (plus one battery powered) saws that I love to use in the city - anytime I am within 100' of anoutlet.
Like fearofpavement notes, there are good electric saws and cheap ones, just like anything else. One of mine, the Makita UC4000, is a 13 amps, well balanced, in-line saw that isn't any louder or heavier than a reciprocating saw, but I have sawn through multiple cords of oak, maple, and other woods with it. It is light, compact, and stores inside; no gas to buy or mix or store. Starts when you pull the trigger; stops when you let go. No heavy hydraulic lines, just a standard extension cord ( I run 12 gauge when I can). I am currently running it with a PowerSharp bar and chain, which has worked out well on it.
**** You still need to buy and use bar oil with these saws and they will still spray some of it off of the tip of the bar if you use them indoors ****
I bought my Makita used from a Home Depot Rental shop for under $100. I figured if it stood up to that type of abuse it would hold up for me. It has been replaced by a newer model, below. STIHL also makes heavy duty electric saws, but I have never tried them. They felt heavy in the store and are priced like other STIHL products. The Makita/Domar, or similar Husqvarna/Jonsered versions sell for $200 -$300 new.
Makita USA - Tool Details - UC4030A
HUSQVARNA 316E Electric - Chainsaws
The 36-40 volt battery-powered saws (Oregon, STIHL) might also be convenient for your use, if you tend to cut wood for limited periods (less than an hour) or purchased a second battery to swap out.
Philbert