We present a study of 16 H I-detected galaxies found in 178 h of observations from Epoch 1 of the COSMOS H I Large Extragalactic Survey (CHILES). We focus on two redshift ranges between 0.108 ≤ z ≤ 0.127 and 0.162 ≤ z ≤ 0.183 which are among the worst affected by radio frequency interference (RFI). While this represents only 10 per cent of the total frequency coverage and 18 per cent of the total expected time on source compared to what will be the full CHILES survey, we demonstrate that our data reduction pipeline recovers high-quality data even in regions severely impacted by RFI. We report on our in-depth testing of an automated spectral line source finder to produce H I total intensity maps which we present side-by-side with significance maps to evaluate the reliability of the morphology recovered by the source finder. We recommend that this become a common place manner of presenting data from upcoming H I surveys of resolved objects. We use the COSMOS 20k group catalogue and extract the filamentary structure using the topological DisPerSE algorithm to evaluate the H I morphology in the context of both local and large-scale environments and we discuss the shortcomings of both methods. Many of the detections show disturbed H I morphologies suggesting they have undergone a recent interaction which is not evident from deep optical imaging alone. Overall, the sample showcases the broad range of ways in which galaxies interact with their environment. This is a first look at the population of galaxies and their local and large-scale environments observed in H I by CHILES at redshifts beyond the z = 0.1 Universe.