We use the H3O+ molecule to investigate the impact of starburst and AGN activity on the chemistry of the molecular interstellar medium. Using the JCMT, we have observed the 3+_2 - 2-_2 364 GHz line of p-H3O+ towards the centers of seven active galaxies. We have detected p-H3O+ towards IC342, NGC253, NGC1068, NGC4418, and NGC6240. Upper limits were obtained for IRAS15250 and Arp299. We find large H3O+ abundances (N(H3O+)/N(H2)>10^{-8}) in all detected galaxies apart from in IC342 where it is about one order of magnitude lower. We note, however, that uncertainties in N(H3O+) may be significant due to lack of definite information on source size and excitation. We furthermore compare the derived N(H3O+) with N(HCO+) and find that the H3O+ to HCO+ column density ratio is large in NGC1068 (24), moderate in NGC4418 and NGC253 (4-5), slightly less than unity in NGC6240 (0.7) and lowest in IC342 (0.2-0.6). We compare our results with models of X-ray and photon dominated regions (XDRs and PDRs). For IC342 we find that a starburst PDR chemistry can explain the observed H3O+ abundance. For the other galaxies, the large H3O+ columns are generally consistent with XDR models. In particular for NGC1068 the elevated N(H3O+)/N(HCO+) ratio suggests a low column density XDR. For NGC4418 however, large HC3N abundances are inconsistent with the XDR interpretation. An alternative possibility is that H3O+ forms through H2O evaporating off dust grains and reacting with HCO+ in warm, dense gas. This scenario could also potentially fit the results for NGC253. Further studies of the excitation and distribution of H3O+ - as well as Herschel observations of water abundances - will help to further constrain the models.