Air carrier First Officer reported another aircraft taxiing in close proximity during taxi. Flight continued.

Narrative

During our taxi out of ORD we were assigned runway 27L/TT after runway 28R/N5 had bad RCC codes with the winds. Due to the nature of the snowstorm we were required to do a pre-takeoff contamination check before we departed. The tower had gave us instructions to taxi up to 27L and hold short of it at B full length. We taxied up there and the FO did the check. Once the FO was done with the check another frequency cleared an Aircraft Y to cross runway 27L on Bravo even though we were still on it. We were not fully on bravo but our nose was sticking into bravo far. ATC had asked if we were on the taxiway which we told them we were. The Aircraft Y elected still to continue taxing right next to our nose and had a close call on the taxiway. We did not get hit by the plane but they were almost off the taxiway trying to get past us on to continue onto their gate.Cause: Poor ATC management letting a plane cross without verifying it was clear; The Aircraft Y crew electing to continue even though they knew it was not a clear taxiway to do so.Suggestions: To mitigate this happening again do not let planes wait on a taxiway you plan to cross other planes on. There could be a wait even though there's no planes. Also verify there is no planes on a taxiway before clearing and crews need to take more caution especially on days where the taxiways and runway conditions aren't the greatest.