We describe a Cs atomic magnetometer operating in the spin-exchange-relaxation-free (SERF) regime. With a vapor cell temperature of $103\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$ we achieve intrinsic magnetic resonance widths $\ensuremath{\Delta}B=17\text{ }\ensuremath{\mu}\text{G}$ corresponding to an electron spin-relaxation rate of $300\text{ }{\text{s}}^{\ensuremath{-}1}$ when the spin-exchange rate is ${\ensuremath{\Gamma}}_{\text{SE}}=14\text{ }000\text{ }{\text{s}}^{\ensuremath{-}1}$. We also observe an interesting narrowing effect due to diffusion. Signal-to-noise measurements yield a sensitivity of about $400\text{ }\text{pG}/\sqrt{\text{Hz}}$. Based on photon shot noise, we project a sensitivity of $40\text{ }\text{pG}/\sqrt{\text{Hz}}$. A theoretical optimization of the magnetometer indicates sensitivities on the order of $2\text{ }\text{pG}/\sqrt{\text{Hz}}$ should be achievable in a $1\text{ }{\text{cm}}^{3}$ volume. Because Cs has a higher saturated vapor pressure than other alkali metals, SERF magnetometers using Cs atoms are particularly attractive in applications requiring lower temperatures.