Is man's ability to reason properly a gift by the Holy Spirit? Is there any Christian denomination that views man's ability to reason properly as a gift by the Holy Spirit?
Most every church recognizes that every good thing is a gift of God, including our reason, but I do not think any denomination assigns the ability to properly reason as a unique ‘gift of the Holy Spirit.  However to reason properly about Christ by faith many churches think can't be done without the enablement of the Spirit. assume by ‘properly’ you mean those There are gifts of the Spirit that are given to the church that make use of proper reason such as the gift of ‘wisdom’ and ‘knowledge’ (1 Cor. 12:8).  The main idea behind these gifts is that 'different' people have been given different ones.  Since all men have reason and by faith can reason properly, it can’t be then a special gift. Pure ability to reason is logically is a natural gift and it is likely, among those without faith, that none excels as high as the Devil, for his powers of reason and knowledge of the external form of religion no man could pretend.  

 So gifts like Teaching, or having wisdom and knowledge naturally relate to our reason and one who has an ‘unusual ability’ by the working of the Spirit, might have a kind of unusual ability to reason about Christ, displaying unusual knowledge or wisdom concerning him and his work.  But as already mentioned these are not recognized as a ‘gift of the Spirit' by any denomination as far as I know.  A person may be said to have his reason ‘on fire’ and under an ‘anointing’ yet this is not with respect to his ability to reason directly.

In fact, what has often marked out spiritual gift is that despite the natural weaknesses of certain men, even without strong powers of reason, people animated by the Holy Spirit have been able to convincingly present the claims of the gospel with extraordinary gifts. In the case of the Apostles who were ‘fisherman’ and who subsequently turned the world over with the gospel, the power of God at work in those real 'unnatural gifts' that he gave them, was seen, in contrast to their power of reason, or natural learning.

I think these and other reasons has kept any church from attributing reason to a gift of the Spirit, just as good-looks, strength and wealth are also not proper gifts.