Tom Westley (57) and Ravi Bopara (61) made half-centuries but lacked support from the rest of their top order.
Just before tea, visiting captain Mark Cosgrove removed Bopara, chopping one of his medium pacers on to the stumps.
Bad light brought play to an early end with Essex on 266-9 - Charlie Shreck (4-79) the pick of the bowlers.
Division Two leaders Essex made a faltering start as Leicestershire's bowlers restricted them with wickets throughout the opening day.