Good compost has a comnination of Greens, browns, air, and moisture (manure is considered a green as it is high in nitrogen. Browns are dead material (like wood chippings and leaves) You generally want a 3:1 Brown:Greens ration...Two much greens create a soggy mess.

That being said, I would create a pile of what you have and add some dead leaves or straw to get the right mixture...turn it once a week for about three months. Then you will have a great compost for the spring. Add a little water to give it moisture, dont let it get soggy. lightly water once a week.
It wouldnt hurt to cover it during wet times this will prevent too much moisture and creating a soggy mess.

Chicken manure is a most nitrogen rich one. I wouldn't put it directly in the garden for few reasons. Nitrogen goes away fast. Added to soil in fall, it will be almost gone by spring. So it is kind of waste of good nitrogen. But what it can actually do, it can help to compost a lot of carbon materials to create organic matter. You soil needs good organics probably more then nitrogen itself. So I second shayneca25 - compost it. If turning it every week seems too much of work - you can leave it as is, it will take about a year to decompose. What also you can do - you can dry some of the staff, better without wood. In summer you can dissolve it in water(Google the proportions!) and use as a great organic fertilizer.

Good advice from the other 2 posters.
I'll add that if you really want to, there is no major problem if you put it in the garden beds this fall. The only issues are that some of the wood chips might still be there in the spring (depending on size and type of wood) and you will lose some of the nitrogen from the manure (as galinas said).

Another option is to put your coop bedding on top of your garden and allow it to decompose over the winter (don't till). Then in the spring, you simply plant in the soil underneath the un-decomposed wood chips and leave the chips on top for mulch.

Since the coop bedding is a combination of manure and wood shavings, and well aged if you only muck once a year, I would put it straight onto the garden, till it in. In the spring it will be well decomposed.
I've actually side dressed things like corn with this stuff straight from the coop, in a thin layer and had great success. I wouldn't use it on legumes and would probably avoid putting it on greens until it's completely decomposed just due to the nitrogen and bacteria issues.