Chevron set to test support, levels to watch Shares are down 1.1% today in a weak energy sector. At the current price of $127.99, next support is at the 10-day moving average which was last at $127.94. Resistance is at $128.96, which was the last value for the 30-day moving average. A breakdown below the 10-day would be bearish for price. Next support in that event would be at $126.42.