They've beaten a Michigan State team ranked third in both polls. They've upset a Kentucky team that began the season favored to win the national title. They've toppled a Louisville team that won last year's championship and may yet get back into contention this winter.
Could North Carolina really miss the NCAA tournament despite those three monumental victories? It's becoming an increasingly realistic possibility.
With Monday night's 76-61 drubbing at the hands of Virginia, North Carolina fell to 1-4 in ACC play for the first time since 2002. Couple that with disappointing non-league losses against Belmont, UAB and Texas, and the Tar Heels are gradually assembling one of the most bizarrely uneven profiles in recent memory.
It's difficult to estimate how many ACC games North Carolina needs to win to land on the right side of the NCAA tournament bubble because the Tar Heels' resumé is so unusual and Selection Sunday is still nearly two months away. Fourteen ACC teams have made the NCAA tournament with sub-.500 league records since expansion to 64 teams in 1986, but North Carolina would be wise not to count on becoming No. 15 since the league is not nearly as strong this season as years past.
For North Carolina to even finish .500 in ACC play, the Tar Heels will have to win eight of their final 13 games against a back-loaded schedule.
The upcoming four-game stretch is manageable with a home game against Clemson, a visit to Georgia Tech and two more home games against struggling Maryland and NC State. It gets harder after that, however, as North Carolina's final nine games include two games apiece against Duke and Notre Dame, a home game against Pittsburgh and visits to Florida State and NC State.
What makes it uncertain whether North Carolina can find a way to squeeze eight more wins out of that schedule is that this Tar Heels team is as flawed as any Roy Williams has coached.
With P.J. Hairston dismissed from the team and consistently Leslie McDonald misfiring from the perimeter, North Carolina is easily the ACC's worst shooting team. The Tar Heels are shooting an anemic 22.7 percent from behind the arc in ACC play and an anemic 57.3 percent from the foul line because point guard Marcus Paige is the only consistent threat from the perimeter on the roster.
Defense and transition offense should be where North Carolina makes up for its inability to shoot from the perimeter and its lack of consistent interior scoring, but the Tar Heels were unable to inflict their will on Virginia on Monday night.
Not only did the Cavaliers keep the pace at their liking the final 30 minutes of the game, they also shot 48.1 percent from the field and committed only eight turnovers. The result was that a close game midway through the first half morphed into a rout a few minutes into the second half as Virginia led by as many as 23 points.
The loss shrank North Carolina's margin for error for the rest of the ACC slate.
Either the Tar Heels must turn things around or they're likely to waste three of the better non-league wins any team has produced this season.