The friendly international was played at Stade de Marrakech in Morocco and was McCarthy's third match in charge of the team.
Kenya had a number of opportunities to claim the win but could ultimately not find a way past the North African side.
Boniface Muchiri was lively for the Harambee Stars and had a good early chance but blazed over from inside the box on six minutes.
William Wilson then headed over a 16th minute Muchiri cross, while the same player was in on goal on the half-hour mark but failed to find the target with just the keeper to beat.
Chad came closest to scoring in the second period when Mahamat Thiam fired in on goal with 58 minutes played, but he somehow dragged his effort wide of the target.
Mbainaissem Jourdain was, meanwhile, on hand to keep out another Wilson effort with the match winding down, leaving Kenya to settle for the draw, ahead of facing Chad again on Tuesday.
McCarthy previously drew 3-3 with The Gambia before losing 2-1 to Gabon in a 2026 World Cup qualifier.
Ahead of the weekend's game assistant coach Anthony Kimani explained that the search for the right mix of players for the national team is still ongoing.
The squad selected by McCarthy was largely made up of local based players as they prepare for the upcoming African Nations Championship, hosted by Kenya, Tanzania and Uganda in August.
He said on Capitol Sports: "As the coach [McCarthy] said earlier on, there is more room for players to come into the team.
"Those who have been selected this time round have a good opportunity to show the coach what they can do and become a part of the team going forward.
"That does not shut the door on those who have not made the team this time round, the national team is always a revolving door."