There is a Hadith in Jame’ Ul Ahadith Wal Maraseel and Kanzul Ummal:
عن أبي بن كعب أن عمر بن الخطاب أمره أن يصلي بالليل في رمضان فقال: إن الناس يصومون النهار ولا يحسنون أن يقرأوا فلو قرأت عليهم بالليل، فقال: يا أمير المؤمنين هذا شيء لم يكن، فقال: قد علمت ولكنه حسن فصلى بهم عشرين ركعة. (ابن منيع).
Translation: Hadhrat Ubai bin Ka‘ab (May Allah be well pleased with him) narrates that Hadhrat Umar commanded him to lead the Salaat Ut Taraweeh in Ramadhan saying that people fast in the day, because of which they cannot recite the Holy Quran properly, it would be better if you recite the Holy Quran in Taraweeh.
He requested: O Commander of the faithful, this is a deed which has not been performed in congregation until now. He (i.e. Hadhrat Umar) said: Yes, I know that, but this is better.
Thus, Hadhrat Ubai bin Ka’ab (May Allah be well pleased with him) led the 20 Raka’at of Taraweeh. (Kanzul Ummal, Hadith No: 23471)
Hadhrat Ubai’s (May Allah be well pleased with him) saying, “This is a deed, which has not been done in congregation until now” means that Taraweeh with congregation for the whole month had not been performed although before this Taraweeh was offered in congregation off and on, as previously mentioned in the Hadith that for 3 or 4 nights, the Sahabah offered Taraweeh in the lead of the Holy Prophet (Sallallahu alaihi wa sallam), then later a group of Sahabah sometimes offered Taraweeh in the lead of Hadhrat Ubai Bin Ka‘ab and the Holy Prophet (Sallallahu alaihi wa sallam) saw it and appreciated it.