Ah, the elusive sleep. It's great that you are coping OK with the chemo; it's never fun but I was the same with AC, life was bearable. Apart from the sleep.
I honestly have no solutions for you ( or I wouldn't be awake at 4 either) I only work part time and I've come to embrace the early hours on the days I don't have to heave myself up the hill to be nice to people. Particularly in this heat.
I'll be heading off for a walk in a couple of minutes then will do some housework when I get home. I've already answered my work emails. Mind you, I live on my own and the Hound hates the vacuum cleaner regardless of what time I use it.
There is a thread 'night howls' where you can often find the sleepless. Mxx