Diagnosis
That leak is almost always from the quick-connect fitting at the base of the filter not being fully pushed onto the faucet's diverter valve stem, or the rubber O-ring inside that fitting is damaged or dirty.
How to Fix It
Turn off the water at the sink. Unscrew the quick-connect fitting (the gray plastic collar) from the filter base by turning it counter-clockwise. Pull the fitting straight off the faucet stem. Check the small black rubber O-ring inside the fitting for cracks or grit. Clean it, re-seat it, or replace it (PUR part # 51387). Push the fitting firmly back onto the faucet stem until it stops, then screw the collar back on tightly.
If That Didn't Work
The leak could be coming from the filter housing itself if it's not locked securely. Make sure the filter cartridge is fully inserted and the housing is turned to the locked position. A cracked housing will also leak and needs replacing.
Heads Up
Don't overtighten the quick-connect collar. Hand-tight is enough. Cranking it with tools can crack the plastic or distort the O-ring, making the leak worse.