Yes, the Orthodox Church believes in the gift of tongues. Read about it.
By Palladius, Bishop of Helenopolis
(Rule of Pachomios, Ch. 15)
And it came to pass that, when the blessed Pachomios was visiting the brethren in their cells, and was correcting the thoughts of each of them, he was obliged to visit a certain Roman, who was a nobleman of high rank, and who knew the Greek language very well. Now therefore, having come to this great man, so that he might exhort him with words which would be beneficial to him, and might learn the motions of his heart, the blessed man spake unto him in the Egyptian tongue, but the brother did not know what the blessed man said. And because the blessed man did not know how to speak Greek, Abba was obliged to call some brother who would be able to interpret to each of them the things which were said by the other.
Now when the brother came to interpret, the Greek did not wish to declare to Abba through others the defects of his heart, and he spoke unto him thus, “After God, I wish you, and you alone, to know the wickednesses of my heart, and I do not desire to declare them unto you through others, for I do not wish that any man except you should hear them.” And when Abba heard these words he commanded the brother who had come to interpret to depart, and because Abba was unable to speak to the Greek brother the words which he wished to say to him about help and redemption, for he knew nothing whatsoever of the Greek language, he made a sign to him with his hand to remain until he came back to him.
Then Abba left him, and went to pray by himself, and he stretched out his hands towards heaven, and prayed to God, saying,
“O Lord, Mighty One, Who sustains the universe, if I am not able to benefit the children of men whom You send unto me from the ends of the earth, because I am not acquainted with their languages, what need is there for them to come? But if You wish them to be saved here through me, give me, O Lord, Star of all creation, the power to know their languages so that I may be able to set their souls in the straight way.”
And when he had prayed for more than three hours and had entreated God to grant him this knowledge, suddenly there was sent from heaven into his right hand something which was like unto a letter written on paper, and when he had read it, he learned immediately how to speak all tongues, and he sent up praise to the Father, and to the Son, and to the Holy Spirit.
And he came with great joy to that brother, and began to talk to him both Greek and Latin with such fluency that when the brother heard him, he said that Abba’s skill in speaking surpassed that of all the learned men. Then Abba corrected him, as was right, and appointed to him the penance which was suitable to his defects, and he committed him to the Lord, and went forth from him.