Here is what I ended up doing to work around the error.
First, I set up the database recovery model as SIMPLE. More information here.
Then, by deleting some old files I was able to make 5GB of free space which gave the log file more space to grow.
I reran the DELETE statement sucessfully without any warning.
I thought that by running the DELETE statement the database would inmediately become smaller thus freeing space in my hard drive. But that was not true. The space freed after a DELETE statement is not returned to the operating system inmediatedly unless you run the following command:
DBCC SHRINKDATABASE (MyDb, 0);
GO
More information about that command here.