Melbourne-headquartered Essential says drilling started about 2pm on Monday and that by 6am Tuesday conductor pipe had been set and the well was drilling ahead at a depth of 23m.
The company expected to take about 10-12 days to reach the target depth of 1650m.
Essential said the East Wing-1 well would follow Ayrford-1.
The Ayrford and East Wing Prospects have the potential to hold between 10 and 20 billion cubic feet of recoverable gas, the company said.
Essential is targeting the onshore extension of the highly productive Pecten High trend, which has offshore discoveries containing more than 400Bcf of recoverable gas in the Waarre Formation at the Casino, Henry and Halladale gas fields.
Early this year, Essential said the Ayrford prospect had 9bcf of associated gas resource and East Wing 5.1bcf of gas at the P50 level of confidence.
Essential owns 100% of the PEP 168 permit.