Update June 2017:
For the past several years I have been using and recommending Minwax Stain in the Natural color #209 for a pretreatment, it is essentially a clear oil , I like to mix just a dash of Helmsman Spar Urethane in Clear Gloss, it must be mixed well and kept mixed as applying , otherwise the spar urethane can settle to the bottom of the can where if this is applied , it will be gummy and not dry leaving a cloudy , gummy residue on the surface.
This mixture should be applied at least twice a week for the first several weeks, at the first sign of any checking, this mixture should be brushed across the top of the crack allowing it to soak into the crack, working down the crack , continue brushing across to get the oil mix to come off the brush into the crack.
After the carving has stabilized and checking seems to be under control, I recommend applying a high quality oil based deck and fence stain, I have been using and recommend Australian Timber Oil by Cabot's, it comes in several colors, I prefer the Natural color, it has an amber tint to protect from UV rays, is quite durable and can help protect the wood from graying due to oxidizing.
After the initial application, this will be applied as needed depending on exposure to the elements, with direct sunlight being the worst.
Any additional cracking that is noticed should be treated as previously with the original Minwax stain in the Natural color #209, if a glossy finish starts to develope , the spar urethane should not be added to the Minwax stain and the Natural color #209 should be applied straight.
Although it is impossible to guarantee that a carving will not crack, proper care and maintenance can limit checking if not prevent it altogether.
Care and preservation treatment process
There is not any one product or any single thing that can be done to a chainsaw carving that will keep it from deteriorating, (drying out, cracking, etc.) but there are any number of things applied together that will significantly delay this deterioration and preserve chainsaw carvings for generations to come.
First and foremost is to keep chainsaw carvings out of the sun, the reason a chainsaw carving cracks is because it dries out too fast, the outer rings of the wood dry and shrink faster than the inside and a crack forms,these are almost unpredictable in where they appear, however there are any number of wood preservation products that can be used to inhibit if not halt the drying process altogether, the most effective of which in my experience and belief is to be the oils, tongue oil, danish oil, teak oil, mineral oil, there are log oils for log cabins, and a product called Cetol by Sikkens.
For the past 3 years I have been using Australian Timber Oil by Cabot's for a topcoat.
Whichever oil is used, please understand for it to be effective, multiple applications are required, thinning with mineral spirits or turpentine helps the oils to soak in.Applications of twice a day for at least a week have shown to stabilize chainsaw carvings.
Indoor pieces might not need reapplication for several years and can be dusted and waxed just as furniture, however with the drier indoor air in the winter there is a higher risk of cracking,reportedly humidifiers reduce the risk.