。
She glanced at her watch nonchalantly.
Literal
She [topic-は] watch [object-を] nonchalantly looked-at.
さりげなく ('casually, nonchalantly, without making a show of it') is the adverbial form of the i-adjective さりげない. The base さり comes from the classical 然り ('so, thus'), with げ ('appearance, look') and ない negating; together, 'with no appearance of intent, as if nothing.' Used for actions you want to do without drawing attention — sneaking a look at one's watch during a long meeting is a textbook example. The image is wonderfully evocative: a glance you hope nobody notices.