VBA, 60 Bytes

i=30:For l=1 To 30:?String(i," ")&"+":i=i+Sgn(Rnd()-.5):Next

Paste it in the Immediate window and hit enter. (Make sure explicit declaration is turned off!)

Far more likely to move than to stay in a line (i.e. actions are not equally weighted) but that was not a specified requirement (Fortunately!)