There is a concept regarding Chanukah called עד שתכלה רגל מן השוק, until there are no longer feet in the market place. This was the rule of thumb to indicate the latest one is allowed to light Chanukah candles.
This means that as long as there are people walking the streets, we are able to fulfill the Mitzva of פרסומי ניסא, advertising the miracle.
The earliest time to light would be from פלג המנחה, which is roughly an hour and a quarter before sunset. This is provided that the candles burn for thirty minutes after צאת הכוכבים, when the stars come out.
The ideal time to light candles is right at צאת הכוכבים, which is at 5:03 today
in Jerusalem. My calendar says, מצוה מן המובחר 5:03, the choicest time is right at צאת. This shows an eagerness to perform the Mitzva at the earliest opportunity. Chag Chanukah Sameach