Thanks goes to ChuckT from the forum for this one. I have used microchips range of Lithium ion battery charger chips before (very low cost and a tiny form factor). They have proven to be a great way of charging 3.7V lithium batteries in my little LED game based devices.
The problem though was that you could either be charging the battery (which means the LED game would be turned off) or you could be playing the game and the battery would be the power source.
ChuckT stumbled upon some excellent information about charging a battery and having the charger provide power to your circuit at the same time ‘load sharing’.
Check out the following link for more info:
and here is a microchip app note with more useful info: