We present a kinematic analysis of the dense molecular gas in the central 200 parsecs of the nearby galaxy NGC 1097 , based on Cycle 0 observations with the Atacama Large Millimeter/sub-millimeter Array ( ALMA ) . We use the HCN ( 4–3 ) line to trace the densest interstellar molecular gas ( n _ { H _ { 2 } } \sim 10 ^ { 8 } cm ^ { -3 } ) , and quantify its kinematics , and estimate an inflow rate for the molecular gas . We find a striking similarity between the ALMA kinematic data and the analytic spiral inflow model that we have previously constructed based on ionized gas velocity fields on larger scales . We are able to follow dense gas streaming down to 40 pc distance from the supermassive black hole in this Seyfert 1 galaxy . In order to fulfill marginal stability , we deduce that the dense gas is confined to a very thin disc , and we derive a dense gas inflow rate of 0.09 M _ { \odot } yr ^ { -1 } at 40 pc radius . Combined with previous values from the H \alpha and CO gas , we calculate a combined molecular and ionized gas inflow rate of \sim 0.2 M _ { \odot } yr ^ { -1 } at 40 pc distance from the central supermassive black hole of NGC 1097 .