We report circular polarization measurements from the first two years of observation with the 40 GHz polarimeter of the Cosmology Large Angular Scale Surveyor (CLASS). CLASS is conducting a multi-frequency survey covering 75% of the sky from the Atacama Desert designed to measure the cosmic microwave background (CMB) linear E and B polarization on angular scales $1^circ lesssim theta leq 90^circ$, corresponding to a multipole range of $2 leq ell lesssim 200$. The modulation technology enabling measurements of linear polarization at the largest angular scales from the ground, the Variable-delay Polarization Modulator, is uniquely designed to provide explicit sensitivity to circular polarization (Stokes $V$). We present a first detection of circularly polarized atmospheric emission at 40 GHz that is well described by a dipole with an amplitude of $124pm4,mathrm{mu K}$ when observed at an elevation of $45^circ$, and discuss its potential impact as a foreground to CMB experiments. Filtering the atmospheric component, CLASS places a 95% C.L. upper limit of $0.4,mathrm{mu K}^2$ to $13.5,mathrm{mu K}^2$ on $ell(ell+1)C_ell^{VV}/(2pi)$ between $1 leq ell leq 120$, representing a two-orders-of-magnitude improvement over previous limits.