The noun chance may be complemented with a marked infinitive (that is, to + the infinitive form of the verb):
I don't even get a chance to show my skills.
In this case, chance means opportunity.
Another collocation is chance of VERBing, where VERBing is the -ing form of a verb. In this case, however, chance means probability:
A flipped coin has a 50% chance of showing heads and a 50% chance of showing tails.
You may very well encounter the of VERBing construction in situations where the opportunity sense is intended. This was at one time acceptable, but died out in the last part of the 19th century; today it is again becoming common in informal discourse, and I would not be surprised to see it become accepted in a generation or two.† For the present, however, it is not accepted in formal discourse.
I recommend that you maintain the distinction strictly in your own writing and speech; the correct uses are perfectly colloquial and will not mark you as pedantic or prim.
† However, I would be surprised to still be around to see it.