remove old chauking from baseboard

I recently had some pergo flooring removed from my upstairs hallway. I will be putting in carpet in the hallway.
The pergo flooring used to have base shoes along the wood baseboard along the walls. Now that the base shoes are removed, there is some old chalking left on the baseboard and most of the chauking is in a groove in the baseboard. I like to remove as much of the old chauking before I patch the paint on the baseboard. This is because the new carpet will be lower than the base shoes and any left over chauking will show above the carpet.
What is the best way to remove the chauking? I have tried to use a chisel and lift up the chauking and then rip it along the groove till the chauking breaks off. Then I repeat the process again down the baseboard. The chauking is about 6 years old and is still pretty taut.
Any recommendation will be much appreciated.

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