The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will observe several Deep Drilling Fields (DDFs) to a greater depth and with a more rapid cadence than the main survey. In this paper, we describe the 'DeepDrill' survey, which used the Spitzer Space Telescope Infrared Array Camera (IRAC) to observe three of the four currently defined DDFs in two bands, centred on 3.6 and 4.5 μm. These observations expand the area that was covered by an earlier set of observations in these three fields by the Spitzer Extragalactic Representative Volume Survey (SERVS). The combined DeepDrill and SERVS data cover the footprints of the LSST DDFs in the Extended Chandra Deep Field-South (ECDFS) field, the ELAIS-S1 field (ES1), and the XMM-Large-Scale Structure Survey field (XMM-LSS). The observations reach an approximate 5σ point-source depth of 2 μJy (corresponding to an AB magnitude of 23.1; sufficient to detect a 1011 M⊙ galaxy out to z ≈ 5) in each of the two bands over a total area of ≈ 29 deg2. The dual-band catalogues contain a total of 2.35 million sources. In this paper, we describe the observations and data products from the survey, and an overview of the properties of galaxies in the survey. We compare the source counts to predictions from the Shark semi-analytic model of galaxy formation. We also identify a population of sources with extremely red ([3.6]-[4.5] >1.2) colours which we show mostly consists of highly obscured active galactic nuclei.