We use two-dimensional Brownian dynamics simulations to study the electrophoresis of a bead-rod chain through a narrow slit. A constant electric field is assumed to act inside and outside of the slit, and each bead on the chain is assigned a constant uniform charge. We calculate the dependence of the polymer transit velocity on chain length, slit dimensions (width-to-length ratio), and electric-field strength. For sufficiently narrow slits, the transit velocity increases nonlinearly with the applied field for low-field strengths, whereas it increases linearly for high-field strengths. In the low-field strength region and for sufficiently narrow slits, the transit velocity decreases rapidly for small chain lengths and then decreases slowly beyond a critical chain length. As the slit width increases, the transit velocity decreases with chain length in more continuous manner, and for sufficiently large slits the transit velocity becomes independent of chain length as expected. Distributions of the chain end-to-end distances and the translocation times depend strongly on the relative size of the chain to the slit. These results show the sensitivity of the transit velocity vs chain length relationship to the slit dimensions and applied electric-field strength, and suggest that there may be an optimal slit width for a given field strength and vice versa. The results may be useful for microfluidic separations and for understanding the motion of biological polymers through narrow constrictions.