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We investigate the contribution of host galaxies to the overall dispersion measures (DMs) for fast radio bursts (FRBs) using the Feedback in Realistic Environments (FIRE-2) cosmological zoom-in simulation suite. We calculate DMs from every star particle in the simulated L * galaxies by ray-tracing through their multiphase interstellar medium, summing the line-of-sight free thermal electron column for all gas elements within ±20 kpc of the galactic midplane. At z = 0, we find average (median) host-galaxy DMs of 74 (43) and 210 (94) pc cm ^−3 for older (≳10 Myr) and younger (≲10 Myr) stellar populations, respectively. Inclination raises the median DM measured for older populations (≳10 Myr) in the simulations by a factor of ∼2 but generally does not affect the younger stars deeply embedded in H ii regions except in extreme edge-on cases (inclination ≳85°). In kinematically disturbed snapshots ( z = 1 in FIRE), the average (median) host-galaxy DMs are higher: 80 (107) and 266 (795) pc cm ^−3 for older (≳10 Myr) and younger (≲10 Myr) stellar populations, respectively. FIRE galaxies tend to have higher DM values than cosmological simulations such as IllustrisTNG, with larger tails in their distributions to high DMs. As a result, FRB host galaxies may be closer (lower redshift) than previously inferred. Furthermore, constraining host-galaxy DM distributions may help significantly constrain FRB progenitor models.