A Celtic victory would take Ronny Deila’s side 12 points clear of Aberdeen who play the first of their remaining four games later in the day against Motherwell at Pittodrie.
However, the goal difference which currently stands at 36 in Celtic’s favour would surely guarantee a fifth successive championship win for the Parkhead club.
US international Kitchen has less than fond memories of the Eastern Conference Championship play-off games for DC United against Houston Dynamo in 2012, when Dynamo won the first game 3-1 before grabbing a 1-1 draw at the RFK Stadium to go through on a 4-2 aggregate and he does not want to experience anything similar this weekend.
The 23-year-old said: “It is huge. I have been part of games where it is a home game and the other team is celebrating on your field.
“In 2012, in the Eastern Conference final, it was the second leg at our place and they beat us on aggregate and were celebrating.
“It is not a good feeling and we will try our best not to allow that to happen.
“That was the last game of the season too. We could have made it to a final which would have been huge, so yes, we don’t want that to happen. There is a lot on the line.”
Kitchen, who signed a two-and-a-half-year deal in March, is looking forward to another battle with Celtic skipper Scott Brown following their meeting at Parkhead earlier in the month which Deila’s side won 3-1.
“He is obviously a good player, a feisty guy who gets into a challenge,” he said.
“So that is good. You like a competitive battle and it is a match-up to look forward to.
“You always want to challenge yourself and play against good players. It is a good experience.
“They are obviously a very good side, lots of talent but, saying that, I thought we played very well, minus the scoreline.
“So that is something we have to clean up and try to mimic the performance.”
Third-placed Hearts go into the game eight points behind Aberdeen with four games remaining.
However, Kitchen is not giving up on a second-place finish and believes playing at Tynecastle this weekend will help.
“It is mathematically still possible,” he said.
“We have to believe. If we don’t believe that then there is no point playing these last games so we have to have that mentality and try to maximise the points and make the most of every opportunity.
“There will be a good atmosphere at the weekend. It is a great environment to be in.
“The fans have been great, very passionate, very supportive and these are the games that are easy to get up for.”
Hearts head coach Robbie Neilson has two key players back for today’s game.
Full-back Juwon Oshaniwa and central defender Igor Rossi return to the squad after missing last week’s defeat at Motherwell through suspension.