Pragyan Gogoi missed a penalty for KBFC in the second half as both sides failed to find the finishing touch in front of the goal.
CFC 'B' got off to a bright start and almost opened the scoring through Rohmingthanga in the seventh minute.
The Mizo striker won the ball in the KBFC half and drew a sharp save from Sujith in the opposition goal.
Chennaiyin had to make a change soon after, with Ajin Tom coming on for the injured Hendry.
CFC B began the second half with intent as Bedashwor tested the keeper with a curled effort from the left.
KBFC, however, posed a threat on the counter attack, keeping the CFC defence on its heels. KBFC had a chance to open the scoring just past the hour mark.
After CFC keeper Sayak Barai was deemed to have brought down substitute John Jacob Kattookaren, Pragyan Gogoi hit wide from the spot kick.
With 15 minutes to go, CFC had the ball in the back of the net courtesy Bedashwor Singh. But the goal was disallowed as Syed Suhail Pasha was deemed to have fouled the KBFC keeper.
CFC B heads back to Chennai with a point, aiming to notch its first win of the campaign on January 19 when it takes on Bengalurus South United FC in a home tie.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)