Particle-in-cell (PIC) schemes have a been a popular method for simulating kinetic plasmas since their inception. However, it has long struggled with so-called “grid heating”, in which the total energy in the system may grow secularly, limiting long-time accuracy. There has been enormous recent progress in implicit PIC methods the feature exact energy conservation, thus solving this problem. However, implicitness comes at the cost of solving a system of equations at each time-step. To that end, we present an explicit PIC scheme that features exact energy conservation. The scheme modifies a relatively standard 2nd-order time integration scheme with an analytically solvable optimization problem for each particle. We confirm that this modification preserves 2nd-order accuracy. Additionally, we derive both electrostatic and electromagnetic versions of the scheme and show that it is compatible with common spatial discretizations used in PIC. Theoretical results are confirmed by numerical experiments applied to standard test problems. Prepared by LLNL under Contract DE-AC52-07NA27344.