Is faith in The Holy Trinity a choice or a gift? In the past and up till now, the majority of humans have believed in some form of deity. Now assume out of all those deities, only the The Holy Trinity is the only true God:


  And this is eternal life, that they know thee the only true God, and Jesus Christ whom thou hast sent. (John 17:3, RSV)


Is faith in The Holy Trinity a choice or a gift? Or is it a combination of both?
If I understand correctly, faith is a theological virtue that God gives to people, as opposed to human virtues that require some human effort to obtain.
http://www.vatican.va/archive/ccc_css/archive/catechism/p3s1c1a7.htm:

1813 ...They [theological virtues] are infused by God into the souls of the faithful to make them capable of acting as his children...
1814 Faith is the theological virtue by which we believe in God and believe all that he has said and revealed to us, and that Holy Church proposes for our belief, because he is truth itself....
1815 The gift of faith remains in one who has not sinned against it...

This gift of faith is then possibly infused during baptism and sealed at confirmation. It may also be obtained by praying to God and asking him for the gift of faith for oneself or for someone else. God can surely also dispense the gift of faith as he pleases without any human intervention according to his will.
To answer your question, it is a combination of both. It starts as a gift, but our human choices determine whether we acknowledge, accept and retain this gift, or whether we sin against, reject and dispose of this gift. God created us to have a free-will, so he won't let us believe something if we don't want to believe it. So I guess the gift of God and our choice to believe will always operate together in some way.