I've been playing with solar power since I was a kid, and believe me when I say that the 1970s were not as ecology friendly as many movements at the time would make you think.
Anyways... You'll need a lot more than you stated here. 24Hour Solar Solution... You will need something similar to a solar power home: Dual Solar Set up with Dual Battery set up and auto-switching capabilities; ie: A Power Switch Board.
The Chip takes what - 950mah? make that 1.2 - 1.5 Ah or 1200 - 1500 mah. Aiming that high to power it will give you some overhead in power.
Now... My research with the Raspberry Pi, a 2400mah cellphone power cell battery will give less than 2 hours on a charge; depending on the R-Pi being used. The Pi-0 and A+ will give almost 3 hours on a 2400mah batter but that is only if they are doing tasks that are not CPU Intensive.
Alright, given that, Rule #1: NEVER EVER(!!!!) Send power to the Chip using the GPIO Headers! NEVER!!! Going back to the Raspberry Pi Universe - this was a hard lesson learned as sending raw power (no matter how filtered or regulated) into the GPIO to power up the Raspberry Pi will give you a Dead R-Pi! GUARANTEED!!! This was a learning issue in that there were some Robotics Kits that Powered the R-Pi through the G-PIO +5V line and BAM! Dead R-Pi was the result. Always send power through the USB Power Port so the power can be properly dealt with by the Chip's Power Regulator System (PSU Circuit).
Don't use Li-Ion Battery Packs. There is a danger that they will burst into flames when over-charging them. Better to use Lead-Gell batteries as used in UPS systems or a Lead-Acid (Motorcycle/Wet) battery. They are safer to use and won't burst into flames when over-charged. Lead Batteries are a lot more robust for this, though Li-Ion batteries will have more power for their size and weight they are flimsy and will fail faster than a Lead Battery.
That is required because you will need to have Double the solar panels; one to run the Chip during the day and the other to charge the battery that was used to run the Chip the night before. And using two batteries is common sense in that you will always have 1 battery charged up while the other is charging. But the problem is having some sort of auto switcher like solar homes use; when one battery is charging, it sets up the other one to be used when the sun goes down then automatically charge that battery during the day and set up the first battery that was charged the day before.
I had a link for a large diy solar panel that did this but lost it. But the closest thing I can find is this youtube video. Hope it helps. The main piece to look at is the solar panel switch module it has; you can get a bigger one online as that one only is capable for 5W.