Try str_detect() from the stringr package, which detects the presence or absence of a pattern in a string.
Here is an approach that also incorporates the %>% pipe and filter() from the dplyr package:
library(stringr)
library(dplyr)
CO2 %>%
filter(str_detect(Treatment, "non"))
Plant Type Treatment conc uptake
1 Qn1 Quebec nonchilled 95 16.0
2 Qn1 Quebec nonchilled 175 30.4
3 Qn1 Quebec nonchilled 250 34.8
4 Qn1 Quebec nonchilled 350 37.2
5 Qn1 Quebec nonchilled 500 35.3
...
This filters the sample CO2 data set (that comes with R) for rows where the Treatment variable contains the substring "non". You can adjust whether str_detect finds fixed matches or uses a regex - see the documentation for the stringr package.