You may legally own this barrel if one of two conditions is true:
1) You own a Remington 870 which is registered with BATFE as either an AOW or SBS
2) You do not own ANY Remington 870's
If you own a Rem 870 which is not registered as either an AOW or SBS, and possess this barrel, you would be violating NFA34, in that BATFE considers you to have "constructive intent". In fact, BATFE has been known to declare that if you own a registered AOW/SBS/SBR and a non-registered example of the same model, you may only possess as many barrels as you have registered NFA weapons for.
For example, you own an 870 registered as a short-barreled shotgun and a non-registered 870 which you use for duck hunting. If you own a 28" bbl for duck and one 13" bbl for the SBS, you're supposedly good to go. However, if you own a 28" bbl for duck, a 13" bbl attached to the SBS, and an extra 13" bbl in the safe, you have the ability to readily turn the second 870 into an unregistered SBS.
This kind of defies logic, because you could just as easily take the 13" bbl off your registered gun and put it on your unregistered gun. This is why some AR-15 SBR owners recommend only owning one lower, the registered SBR.
Of course, this assumes that you give a BATFE agent cause to question you about the length of your shotgun bbl. If you were to use it in a home-defense situation, you can rest assured that you'll be spending the next several years in Club Fed. If you take it to the range for some fun, you run a very small chance of some LEO asking you about it. If you keep it in the basement and only take it out to pop off a few rounds, alone, on your very large farm, where you have few, if any, neighbors, you probably don't have much to worry about.
Remember, if you do choose to violate NFA34, they can put you in Federal prison, take away your guns and voting rights, and mess up the rest of your life but good.