High resolution X-ray spectroscopy of the warm absorber in the nearby X-ray bright Seyfert 1 galaxy, Mrk 1040 is presented. The observations were carried out in the 2013-2014 timeframe using the Chandra High Energy Transmission Grating with a total exposure of 200 ks. A multitude of absorption lines from Ne, Mg and Si are detected from a wide variety of ionization states. In particular, the detection of inner K-shell absorption lines from Ne, Mg and Si, from charge states ranging from F-like to Li-like ions, suggests the presence of a substantial amount of low ionization absorbing gas, illuminated by a steep soft X-ray continuum. The observations reveal at least 3 warm absorbing components ranging in ionization parameter from $\log\xi = 0-2$ and with column densities of $N_{\rm H} =1.5-4.0 \times 10^{21}$cm$^{-2}$. The velocity profiles imply that the outflow velocities of the absorbing gas are low and within $\pm100$ km s$^{-1}$ of the systemic velocity of Mrk 1040, which suggests any outflowing gas may have stalled in this AGN on large enough scales. The warm absorber is likely located far from the black hole, within 300 pc of the nucleus and is spatially coincident with emission from an extended Narrow Line Region as seen in the HST images. The iron K band spectrum reveals only narrow emission lines, with Fe K$\alpha$ at 6.4 keV consistent with originating from reflection off Compton thick pc-scale reprocessing gas.