You probably will have to leave early, but it is only three or four Tube stops (eight to ten minutes) from Chalk Farm to Kings Cross so it shouldn't take too long to get from one to the other.
Transport for London Journey Planner
You'll be going from Chalk Farm to Kings Cross St Pancras. You'll need to make sure that the train you catch is posted as "Morden via Bank" - the other trains don't go through Kings Cross St Pancras. The ones you want leave Chalk Farm at 22:58, 23:05 and 23:13 - any later than that and you risk missing the train back up to Leeds.