They made the trade with the Senators not to get Zaitsev, but to get a 2nd round pick for taking on his contract, which was absolutely a great move by Kyle Davidson.
Ben Pope, of the Chicago Sun-Times, has provided us with statistics of Zaitsev's first 3 games in Chicago. He states that it is stats from his first 6 games, but corrected himself in the comments and said that it was the first 3:
Zaitsev has clearly not been doing well, but that should be alright with fans, as it is tanking season in Chicago.