"We have the idea that God rewards us for our faith, and it may be so in the initial stages."
In one sense, the most explicit reason to suggest that God does not reward our faith is that it is a GIFT! We do not receive it as a trade, but as a part of His glorious grace!
"For by grace are ye saved through faith; and that not of yourselves: it is the gift of God" (Ephesians 2:8)
Yet, Chamber's line does not fit neatly with the Promise offered in Hebrews:
"But without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him."(Hebrews 11:6)
God does reward us for our faith! He is constantly showering us with His love and His goodness. We miss out on his blessings the moment we begin to think that we deserve his blessings, or that we must earn them in some way. Then we cannot enjoy because we are not receiving them. By faith alone, we receive this grace, and this grace covers everything, not just salvation for eternity, but a blessed life here on Earth:
"What shall we then say to these things? If God be for us, who can be against us?
"He that spared not his own Son, but delivered him up for us all, how shall he not with him also freely give us all things?" (Romans 8:31-32)