But a number of Leicestershire batsmen got starts and then got out as they lost wickets at regular intervals.
Debutant Callum Parkinson took 3-64 as four Leicestershire men were out in the 40s, before Eckersley's patient innings helped them rebuild.
He hit seven fours as Leicestershire ended the first day on 300-7.
Ned Eckersley hit an unbeaten 73 as Leicestershire enjoyed a decent opening day with the bat against Derbyshire at Grace Road.