Ajax only needed a draw to ensure they qualified for the last 16, but the Blues were in search of the three points that would guarantee them a qualification spot.
Both sides played some exciting football on the night, with Chelsea frontman Islam Feruz and Ajax centre forward Queensy Menig both having plenty of opportunities to give their side the lead.
The draw means Chelsea will qualify should Anderlecht or Liverpool fail to win their last remaining game, but should they do so they will need a point in Amsterdam in the reverse fixture to qualify for the last 16.
Olympiacos edged out Athletic Club 1-0 to book their place in the last 16 at the Karaiskakis stadium.
In a must win game for the home side, Olympiacos started very well and used the width of the pitch to stretch Athletic. The hosts created several opportunities early on and, just after the half-hour mark, Dmitri Gino slotted past Kepa Arrizabalada to make it 1-0.
Athletic Club looked stunned at going behind, and struggled to get back into the game, knowing that defeat would knock them out of the tournament.
The Greek side held off some heavy pressure late on to ensure they booked their place in the last 16 as Group winners ahead of Arsenal.