Promoted to open, the 24-year-old made 126 off 147 balls, with two sixes off spinner Zafar Ansari and 18 fours.
He shared a stand of 120 with Ben Raine (57), but the last five wickets went for 17 as they were all out for 292.
Matt Dunn claimed 4-72 for Surrey and Kevin Pietersen made 35 not out as they ended the day well-placed on 105-2.
Pietersen will be looking for a big innings on the second day to send a message to Andrew Strauss - England's newly appointed director of cricket - ahead of the summer Test series against New Zealand and Australia.
He has only managed scores of 19, 53 not out, 32 and eight not out since starting the summer with a century against Oxford MCCU, but an unbroken stand of 54 with Sri Lanka international Kumar Sangakkara (also 35) put Surrey in a healthy position overnight.
Surrey fast bowler Matt Dunn:
"As a bowling unit we applied pressure throughout. They had a really good partnership in the middle, which set us back a bit.
"Lewis Hill played really well, but I think we kept them to what we think is a below par score."
Leicestershire opener Lewis Hill:
"My heart rate was going quite fast in the nineties, but Ben Raine did a great job calming me down.
"The idea was to be positive and pounce on anything loose. I was disappointed to get out when I did. I probably lost my concentration a little bit."
Lewis Hill scored his maiden first-class century in only his second appearance for Leicestershire on the opening day against Surrey at The Oval.