The New Catholic Encyclopedia states: "The formulation 'one God in three Persons' was not solidly established, certainly not fully assimilated into Christian life and its profession of faith, prior to the end of the 4th century. But it is precisely this formulation that has first claim to the title 'the Trinitarian dogma'. Among the Apostolic Fathers, there had been nothing even remotely approaching such a mentality or perspective."-(1967), Vol. XIV, p. 299.
Just to be clearer on the teachings of the Catholic Church - this is not fully in context.
http://www.newadvent.org/cathen/15047a.htm
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The Trinity is the term employed to signify the central doctrine of the Christian religion -- the truth that in the unity of the Godhead there are Three Persons, the Father, the Son, and the Holy Spirit, these Three Persons being truly distinct one from another.
Thus, in the words of the Athanasian Creed: "the Father is God, the Son is God, and the Holy Spirit is God, and yet there are not three Gods but one God." In this Trinity of Persons the Son is begotten of the Father by an eternal generation, and the Holy Spirit proceeds by an eternal procession from the Father and the Son. Yet, notwithstanding this difference as to origin, the Persons are co-eternal and co-equal: all alike are uncreated and omnipotent. This, the Church teaches, is the revelation regarding God's nature which Jesus Christ, the Son of God, came upon earth to deliver to the world: and which she proposes to man as the foundation of her whole dogmatic system.
In Scripture there is as yet no single term by which the Three Divine Persons are denoted together. The word trias (of which the Latin trinitas is a translation) is first found in Theophilus of Antioch about A.D. 180. He speaks of "the Trinity of God [the Father], His Word and His Wisdom (To Autolycus II.15). The term may, of course, have been in use before his time.
Afterwards it appears in its Latin form of trinitas in Tertullian (On Pudicity 21). In the next century the word is in general use. It is found in many passages of Origen ("In Ps. xvii", 15). The first creed in which it appears is that of Origen's pupil, Gregory Thaumaturgus. In his Ekthesis tes pisteos composed between 260 and 270, he writes:
There is therefore nothing created, nothing subject to another in the Trinity: nor is there anything that has been added as though it once had not existed, but had entered afterwards: therefore the Father has never been without the Son, nor the Son without the Spirit: and this same Trinity is immutable and unalterable forever (P.G., X, 986).
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So, there was historically, from very early in the Church teachings on God being a Trinity of persons.
You can go online and read the rest at the link above, if you like, although it is in more scholarly language in this edition!
ADDENDUM: It also has explanations of the Trinity in both the Old and New Testaments further down in the article and in the traditions of the early Christians. Its pretty long and while it is a little scholarly, I am able to understand it so no one should have too much trouble with it.
EDITED to add a thought I hadn't thunk until later.