The Torah and the Gemara (especially in Yoma) gives us fascinating detail about the bigdei kahuna (clothes of the priests) that were worn in the Holy Temple. What is not clear is whether tefillin were worn by the kohanim when they performed their services. Do we have any sources that confirm whether or not kohanim indeed wore tefillin during their avodah?
The Talmud (Arachin 3b) informs us that the Kohanim were exempt from wearing the Tefillah shel Yad while servicing in the Temple because it would constitute a separation between the priestly garments and the skin. The Tefillah shel Rosh could still be worn, and the priestly garments on the head were worn in such a way as to leave room in the front for the Tefillah shel Rosh. However, the Talmud (Zevachim 19a) also tells us that Kohanim, Leviyim and Yisraelim who were serving in the Temple were exempt from wearing Tefillin, as Rashi there explains, because of the principle עוסק במצווה פטור מן המצווה one who is busy with one Mitzva is exempt from another. Rambam (Klei Hamikdash 10:6) says that the Kohanim could wear the Tefillah shel Rosh during the Temple service if they wanted to.
רש"י (שמות כ"ח ל"ז) describes the placement of the straps on the ציץ that was worn by the כהן גדול to be consistent with wearing תפילין at the same time.
על פתיל תכלת. ובמקום אחר הוא אומר ויתנו עליו פתיל תכלת? ועוד כתיב כאן והיה על המצנפת, ולמטה הוא אומר והיה על מצח אהרן. ובשחיטת קדשים שנינו שערו היה נראה בין ציץ למצנפת ששם מניח תפלין