Abstract: A mobile marine drilling unit comprising: a floatable base; a floatable platform; and a vertical support leg attached to said base and extending upwardly through a well provided therefor in said platform. Said base and a major portion of said leg being submergible in a body of water for support on the floor thereof. The support leg and platform are provided with elevating mechanisms for elevating the platform above said body of water on said leg. In deploying the drilling unit, the unit is floated to a selected site with the base drawn up underneath the platform and the leg extending upwardly through the well. When the site is reached the base is submerged with ballast until it is supported on the water body floor. Then the platform is elevated above the water body by the elevating mechanisms. A derrick may be moved over the leg well and drilling in the water body floor conducted through the well and leg.