Lidoda Duvha were overall the stronger team, though they failed to make the most of the chances they created, particularly in the second half when really took control of the game and pinned the visitors back in their own half.
The draw represents the Chilli Boys' first point in the top flight after losing their first two matches. They were the better team in the first stanza, but faded as an attacking force as the game went on.
One would have expected Leopards to dominate from the early stages on their own home turf, but while they may have enjoyed the greater share of ball possession, it was in fact Chippa who created the better chances in the first half.
Within the first 10 minutes, Sibusiso Mnguni shot just over the target from a free kick before Mxolisi Ntshingila had a clear sight of goal but ballooned his effort over the crossbar, much to the relief of goalkeeper Ayanda Mtshali.
Chippa captain Gift Sithole also had a chance to put his team ahead within the first quarter hour, but he failed to direct his header on target after the hosts had failed to clear their lines from a Chippa set piece.
Mtshali was called upon to make a decent save just before the break, tipping a dipping long range effort from Diego Brown over the crossbar to leave the score locked at 0-0 heading into the interval.
Leopards started the second half strongly and midfielder Raymond Monama almost opened the scoring on 49 minutes with a free-kick that had the beating of Chippa's nervous-looking keeper Daouda Kassaly, but rebounded off the upright.
On 69 minutes Rodney Ramagalela tried an acrobatic volley after being picked out by a good cross from the right flank, but he stubbed his effort straight into the ground and Kassaly was able to turn the ball away from goal for a corner kick.
Leopards continued to create chances right up to the dying minutes of the game, but they never did enough to really stretch Kassaly or the backline in front of him, leaving the match to end as a goalless stalemate.