With the proliferation of consumer-level virtual reality (VR) devices, users started experiencing VR in less controlled environments, such as in social gatherings and public areas. While the current VR hardware provides an increasingly immersive experience, it ignores stimuli originating from the physical surroundings that distract users from the VR experience. To block distractions from the outside world, many users wear noise-canceling headphones. However, this is insufficient to block loud or transient sounds (e.g., drilling or hammering) and, especially, multi-modal distractions (e.g., air drafts, temperature shifts from an A/C, construction vibrations, or food smells). To tackle this, we explore a new concept, where we directly integrate the distracting stimuli from the user's physical surroundings into their virtual reality experience to enhance presence. Using our approach, an otherwise distracting wind gust can be directly mapped to the sway of trees in a VR experience that already contains trees. Using our novel approach, we demonstrate how to integrate a range of distractive stimuli into the VR experience, such as haptics (temperature, vibrations, touch), sounds, and smells. To validate our approach, we conducted three user studies and a technical evaluation. First, to validate our key principle, we conducted a controlled study where participants were exposed to distractions while playing a VR game. We found that our approach improved users' sense of presence, compared to wearing noise-canceling headphones. From these results, we engineered a sensing module that detects a set of simple distractive signals (e.g., sounds, winds, and temperature shifts). We validated our hardware in a technical evaluation and in an out-of-lab study where participants played VR games in an uncontrolled environment. Moreover, to gather the perspective of VR content creators that might one day utilize a system inspired by our findings, we invited game designers to use our approach and collected their feedback and VR designs. Finally, we present design considerations for mapping distracting external stimuli and discuss ethical considerations of integrating real-world stimuli into virtual reality.