Well that depends on who you ask. So let's have a look:
We read in the Torah, "This shall be fringes for you, and when you see it, you will remember all the commandments of the Lord to perform them. And you will not turn after your heart and after your eyes, after which you tend to stray …"1
Accordingly, Rabbi Yosef Caro (1488-1575) writes in his Shulchan Aruch that one should wear the tzitzit over his other garments so that he can constantly see them and be reminded of the mitzvot.2
In this same tradition, Rabbi Israel Meir Kagan (1838-1933), known as the Chafetz Chaim, strongly objected to those who tucked the actual fringes of their tzitzit into their pants. He wrote that doing so is a denigration of the mitzvot. He compared the tzitzit to an autographed gift from a king which the recipient would surely want to wear in the most visible manner.3
On the other hand, the great Kabbalist, Rabbi Isaac Luria (the Arizal, 1534-1572), would wear his tallit kattan, tzitzit and all, under his other garments. His protégé, Rabbi Chaim Vital explained that this was because the tallit kattan and the tallit gadol relate to two kinds of reality: the internal reality (pnimiut) and the external reality (chitzuniut). The tallit kattan represents the internal level and is therefore worn within other garments, while the tallit gadol represents the external and is therefore worn over the other garments.4
In a published talk, the Rebbe elucidated this concept, explaining that in the "external reality" of the talit gadol, when the Torah says to see the tzitzit, it means actual, external visibility, because this will affect your external behavior, keeping you from sin and reminding you to fulfill all the mitzvahs. In the "internal reality" of the tallit kattan, however, seeing the tzitzit means looking internally towards your own inner self, carrying yourself to a higher level of spirituality and fulfillment of the mitzvahs.5
Many Sephardim base their practice on this precedent of Rabbi Isaac Luria and tuck their tzitzit into their pants. They fulfill the obligation of actually "seeing" the tzitzit through wearing their tallit gadol over the other garments.
On the other hand, Rabbi Schneur of Liadi (1745-1812) writes in his authoritative Shulchan Aruch Harav that even if one does wear the garment under his shirt, he should leave the actual fringes hanging out so that they serve as a constant reminder.6 This is the common Chabad practice today.
In that same above-mentioned talk, the Rebbe points out that Rabbi Isaac Luria's custom is not an instruction to others, but his own personal conduct. This is because on the Arizal's level, a look inward was sufficient. For the rest of us, especially today, we need to actually see those tzitzit to remember all the mitzvot and not stray after our hearts and after our eyes, after which we are quite inclined to stray. Therefore, even though the Arizal kept his tzitzit in, today we need to keep them out and visible.
Some practical advice: If you wish to fulfill the mitzvah this way, but are worried about soiling the tzitzit at work, or just looking sloppy, try tucking them under your belt and then into your pants pockets. This way, they are still visible, but stay neat and tidy.
Please let me know if this helps,
Yours truly,
Rabbi Menachem Posner
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