And as often is the case in professional sports, they chose to gamble that Chapman's performance on the mound will outweigh any negative effects of baseball's ongoing investigation into an alleged violent incident involving the star closer and his ex-girlfriend.
It may be a disturbing way to deal with a player accused of domestic violence, but in reality, the Yankees have no reason to do otherwise.
There's little doubt that there was some type of altercation in October between Chapman and his ex-girlfriend at his home in Davie, Florida, and in response to whatever happened, Chapman not only fired eight shots from a handgun in his own garage (which he admitted to police), but he also smashed his left fist into the window of his SUV.
And yet, the police report of the Oct. 30, 2015, incident, as well as a half-dozen supplemental reports by Broward County investigators, are inconclusive, enough that the Yankees could see only what they wanted to see: Chapman, a left-hander who throws a fastball clocked at 104 mph, could be had cheaply because of the cloud of a domestic violence allegation over his head.
According to the original police report, which Chapman publicly acknowledged is accurate, the weapons involved were "HANDS/FIST/FEET/TEETH." The disturbance was raucous enough that more than a dozen police officers were dispatched to the scene, and they "established a perimeter" around Chapman's 10,000-square-foot home to prevent anyone from escaping.
But what actually happened that night? Only the participants, as well as some family witnesses, know. Unlike the case involving former NFL running back Ray Rice, there is no videotape of the incident. No police officer witnessed any acts of violence. And the testimony of witnesses is maddeningly contradictory.
The woman told police that Chapman choked her, although not to the point of restricting her breathing. Chapman acknowledged only poking her in the shoulder with his index and ring finger. According to the police report and two of the supplemental reports, "there were no injuries or even redness" on the neck or chest of the woman, whose name is redacted from all records of the incident.
In fact, the only documented injury was to a knuckle on Chapman's left pinkie, which was scraped when he punched the car window.
As a result of the lack of physical evidence -- as well as what investigators termed "inconsistencies" in the woman's story, and her ultimate refusal to prosecute -- Chapman has not, and will not, be charged with either domestic violence or a gun violation.
This is not to minimize the crime of domestic violence, or to blame the victim or to conclude that Chapman did not do a despicable thing that night. All it reminds you of is how slippery a slope we walk when confronted with the conflicting stories in such cases, and how easy it is to jump to conclusions one way or the other.
And if nothing else, his potentially deadly temper tantrum alone -- one of the eight gunshots flew through a window and might well have hit someone unlucky enough to be in its path -- raises questions about Chapman's emotional fitness.
That goes beyond the question of whether Chapman can handle closing games in the pressure cooker of the ninth inning at Yankee Stadium -- or Fenway Park or the Rogers Centre, for that matter.
Given the facts available to them, it is as difficult to condemn the Yankees for acquiring Chapman, probably the premier relief pitcher in baseball, for a quartet of minor leaguers, as it is to laud the Los Angeles Dodgers for pulling out of a similar deal when the allegations first came to light in December.
Professional sports is a business, and often a dirty business, and as objectionable as it may seem, the roster of every team in every major sport might contain more than one guy you would not want dating your daughter.
Chapman may well be one of those guys, and for Yankees manager Joe Girardi, the father of two young daughters, it is both his blessing and his curse to have him on the roster this season.
On the one hand, adding Chapman to a bullpen that already boasts Andrew Miller and Dellin Betances potentially gives the Yankees not only the best late relief in the game, but also the ability to effectively shorten their games to six-inning affairs.
On the other hand, Girardi may find himself defending the type of character who is not worthy of his defense and whose behavior can only be worsened by any enabling.
That is why Girardi grew increasingly uncomfortable under a half-hour of questioning Thursday, the day pitchers and catchers reported to a Yankees camp supposedly devoid of controversy.
He acknowledged the horror of domestic violence. He obliquely invoked his deep religious beliefs when he said, "I think it's important for me to be there for him." He expressed his own concerns as a father trying to teach the proper ways of behavior to his daughters and his son as they enter adolescence.
Girardi also confessed that, even though the Chapman case has been classified "inactive" by the Broward County Police, if Major League Baseball chooses to suspend Chapman, he would have no objection to it.
"I think there's an expectation of conduct and how you're supposed to handle situations that maybe in the court of law is different than the court of Major League Baseball's opinion or the players' association's opinion or the public's opinion," Girardi said. "I understand that. I think we have a responsibility as athletes on the way we present ourselves on and off the field, and I'm OK with that."
At the same time, he sure loves having that high-octane arm in his bullpen.
"I think adding Chapman to that bullpen mix is really good," Girardi said. "Our bullpen, especially that final three, were really, really good last year, but now I think it has a chance to be even better."
It would have been interesting to hear how Girardi's predecessor, Joe Torre, would have handled this situation, considering his own experiences with domestic violence -- as a boy, he witnessed his mother being abused by his father -- balanced against his own tendency, like Girardi, to defend his players at almost any cost.
But MLB, understandably, chose not to make Torre available due to his involvement with its ongoing investigation, which it also will not comment on. However, Yankees officials who have spoken to me off the record expect Chapman to get some kind of suspension under the league's new domestic violence policy by commissioner Rob Manfred, if only to make a public display of the differences between MLB and the NFL, and the clumsy way in which commissioner Roger Goodell handled the Rice case.
Still, Girardi went ahead and named Chapman his closer, even if it is likely he will not start the season on the active roster.
"Whether he's suspended or not is not up to me," Girardi said. "I don't have the information; I don't have a police report, I wasn't there. It's really hard for me to make an assessment. I'm concerned about our team and the team we're playing. Part of a manager's job is to manage the players that they give you."
In Aroldis Chapman, the Yankees gave Joe Girardi a potential gold mine this winter. They also gave him a likely season full of headaches, as well as a moral quandary that no manager in his right mind would ever want to wrestle with.