Hi aus-aviator
Chances are there. First hassle is a work permit, you can do without it for a while but you need it, or a residence permit. For the latter you have to be married for 2 years.
Several companies there looking for expat pilots Aerosvit for one needs people for their expanding 767 operation. Time and experience on type required, considerable experience that is. Wizzair Ukraine has had foreigners flying there on validations. Again you would need to have an A320 type and time on it.
As for entry level jobs. These are non-existent. Aviation for such a large country is in it's infancy but with huge potential.
I'll ask around in Kiev today.