We present MCSED, a new spectral energy distribution (SED)-fitting code, which mates flexible stellar evolution calculations with the Markov Chain Monte Carlo algorithms of the software package emcee. MCSED takes broad, intermediate, and narrow-band photometry, emission-line fluxes, and/or absorption line spectral indices, and returns probability distributions and co-variance plots for all model parameters. MCSED includes a variety of dust attenuation curves with parameters for varying the UV slopes and bump strengths, a prescription for continuum and PAH emission from dust, models for continuum and line emission from ionized gas, options for fixed and variable stellar metallicity, and a selection of star formation rate (SFR) histories. The code is well-suited for exploring parameter inter-dependencies in sets of galaxies with known redshifts, for which there is multi-band photometry and/or spectroscopy. We apply MCSED to a sample of $sim2000$ $1.90<z<2.35$ galaxies in the five CANDELS fields, which were selected via their strong [O III] $lambda5007$ emission, and explore the systematic behavior of their SEDs. We find the galaxies become redder with stellar mass, due to both increasing internal attenuation and a greater population of older stars. The slope of the UV extinction curve also changes with stellar mass, and at least some galaxies exhibit an extinction excess at 2175 Angstroms. Finally, we demonstrate that below $Mlesssim10^9,M_{odot}$), the shape of the star-forming galaxy main sequence is highly dependent on the galaxies assumed SFR history, as calculations which assume a constant SFR produce stellar masses that are $sim1$ dex smaller than those found using more realistic SFR histories.
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