Boss Jeff King says Chelmsford need to keep their feet on the ground despite being top of the Conference South.
The Clarets hold a six-point advantage over Eastleigh following their 2-1 defeat of Hayes & Yeading on Saturday.
King told BBC Essex: "Six points is great and also to be top at Christmas, but we can't go thinking we don't need to be trying now.
"We must keep our feet on the ground - we won our league last year and we've just to keep going."
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King added: "It's a great prize to win this league for a club that three years ago was struggling."
Chelmsford continue their promotion challenge over the Christmas period with a double-header against local rivals Thurrock.
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